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Smarandache Geometries and Curves

An axiom is said smarandachely denied if in the same space the axiom behaves differently (i.e., validated and invalided; or only invalidated but in at least two distinct ways). Therefore, we say that an axiom is partially negated, or there is a degree of negation of an axiom.



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Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to find combinatorial behavior for objectives. Recently, such research works appeared on journals for mathematics and theoretical physics on cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics,...
Smarandache Geometries and Curves
by Atakan Tulkan Yakut; Murat Savas; Tugba Tamirci
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We introduce special Smarandache curves based on Sabban frame and we investigate geodesic curvatures of Smarandache curves on de Sitter and hyperbolic spaces.The existence of duality between Smarandache curves on de Sitter space and Smarandache curves on hyperbolic space is shown. Furthermore, we give examples of our main results.
Smarandache Geometries and Curves
by Melih Turgut; Suha Yilmaz
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A regular curve in Minkowski space-time, whose position vector is composed by Frenet frame vectors on another regular curve, is called a Smarandache Curve. In this paper, we define a special case of such curves and call it Smarandache TB2 Curves.
Smarandache Geometries and Curves
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The Scientific Elements is an international book series. This series is devoted to the applications of Smarandache’s notions and to mathematical combinatorics. These are two heartening mathematical theories for sciences and can be applied to many fields. This book selects 12 papers for showing applications of Smarandache's notions, such as those of Smarandache multi-spaces, Smarandache geometries, Neutrosophy, etc. to classical mathematics, theoretical and experimental physics, logic,...
Smarandache Geometries and Curves
by Yanpei Liu
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A map is a 2-cell decomposition of surface, which can be seen as a connected graphs in development from partition to permutation, also a basis for constructing Smarandache systems, particularly, Smarandache 2-manifolds for Smarandache geometry. As an introductory book, this book contains the elementary materials in map theory, including embeddings of a graph, abstract maps, duality, orientable and non-orientable maps, isomorphisms of maps and the enumeration of rooted or unrooted maps,...
Smarandache Geometries and Curves
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A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache n-manifold is a nmanifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equilateral triangular disks on a plane and a more general way for Smarandache 2-manifolds on surfaces,...
Smarandache Geometries and Curves
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In this paper, we investigate special spacelike Smarandache curves of timelike curves according to Sabban frame in Anti de Sitter 3-Space. Moreover, we give the relationship between the base curve and its Smarandache curve associated with theirs Sabban Frames. However, we obtain some geometric results with respect to special cases of the base curve. Finally, we give some examples of such curves and draw theirs images under stereographic projections from Anti de Sitter 3-space to Minkowski...
Smarandache Geometries and Curves
by Rajesh Kumar T.J.; Mathew Varkey T.K.
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In this paper, we discuss the adjacency matrices of graceful digraphs such as unidirectional paths,alternating paths,many orientations of directed star and a class of directed bistar. We also discuss the adjacency matrices of unidirectional paths and alternating paths if they are odd digraceful.
Smarandache Geometries and Curves
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Topological and differential structures such as those of d-pathwise connected, homotopy classes, fundamental d-groups in topology and tangent vector fields, tensor fields, connections, Minkowski norms in differential geometry on these finitely combinatorial manifolds are introduced. Some classical results are generalized to finitely combinatorial manifolds. Euler-Poincare characteristic is discussed and geometrical inclusions in Smarandache geometries for various geometries are also presented...
Integral theory on these smoothly combinatorial manifolds are introduced. Some classical results, such as those of Stokes’ theorem and Gauss’ theorem are generalized to smoothly combinatorial manifolds in this paper.
Smarandache Geometries and Curves
by L. Kuciuk; M. Antholy
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In this paper we make a presentation of these exciting geometries and present a model for a particular one.
This book is for students and young scholar, words of a mathematician, also a physicist and an economic scientist to them through by the experience himself and his philosophy. By recalling each of his growth and success steps, i.e., beginning as a construction worker, obtained a certification of undergraduate learn by himself and a doctor’s degree in university, promoting mathematical combinatorics for contradictory system on the reality of things and economic systems, and after then...
Smarandache Geometries and Curves
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In this work, we introduce some special Smarandache curves in the Euclidean space. We study Frenet-Serret invariants of a special case. Besides, we illustrate examples of our main results.
Smarandache Geometries and Curves
by Clifford Singer
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Of the branches of mathematics, geometry has, from the earliest Hellenic period, been given a curious position that straddles empirical and exact science. Its standing as an empirical and approximate science stems from the practical pursuits of artistic drafting, land surveying and measuring in general. From the prominence of visual applications, such as figures and constructions in the twentieth century Einstein’s General Theory of Relativity holds that the geometry of space-time is...
Smarandache Geometries and Curves
by Murat Savas; Atakan Tugkan Yakut; Tugba Tamirci
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In this study, we give special Smarandache curves according to the Sabban frame in hyperbolic space and new Smarandache partners in de Sitter space. The existence of duality between Smarandache curves in hyperbolic and de Sitter space is obtained. We also describe how we can depict picture of Smarandache partners in de Sitter space of a curve in hyperbolic space. Finally, two examples are given to illustrate our main results.
Smarandache Geometries and Curves
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On a geometrical view, the conception of map geometries is introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surfaces. Some open problems related combinatorial maps with the Riemann geometry and Smarandache geometries are presented.
Smarandache Geometries and Curves
by S. Bhattacharya
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A Smarandache Geometry is a geometry which has at least one Smarandachely denied axiom. It was developed by Florentin Smarandache since 1969 in his paper on Paradoxist Mathematics. We say that an axiom is Smarandachely denied if the axiom behaves in at least two different ways within the same space (i.e., validated and invalided, or only invalidated but in multiple distinct ways). As a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and Riemannian geometries may be united altogether, in...
Smarandache Geometries and Curves
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Parallel lines are very important objects in Euclid plane geometry and its behaviors can be gotten by one’s intuition. But in a planar map geometry, a kind of the Smarandache geometries, the situation is complex since it may contains elliptic or hyperbolic points. This paper concentrates on the behaviors of parallel bundles in planar map geometries, a generalization of parallel lines in plane geometry and obtains characteristics for parallel bundles.
Smarandache Geometries and Curves
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In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and the uses in various fields, we are interested here to study a special kind of curves called Smarandache curves in Lorentz 3-space. Then, we present some characterizations for these curves and calculate their Darboux invariants. Moreover, we classify TP, TU, PU and TPU-Smarandache curves of a spacelike curve according to the...
Smarandache Geometries and Curves
by Samir K. Vaidya; Raksha N. Mehta
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In this paper we explore the concept of strong domination number and investigate strong domination number of some cycle related graphs.
Hu Chang-Wei considers through analysis on the basis of the derivation of the Lorentz transformation by means of fluid mechanics, that Newtonian absolute space-time theory is most basic and real space-time theory, where the physical vacuum is a compressible superfluid, a change of its density can cause a change of actual space-time standards, and thus, leads up to the quantitative effect deviated absolute space-time theory. The effects of relativity and quantum are all quantitative effects, and...
Smarandache Geometries and Curves
by Howard Iseri
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A paradoxist geometry focuses attention on the parallel postulate, the same postulate of Euclid that Gauss, Bolyai, Lobachevski, and Riemann sought to contradict. In fact, Riemann began the study of geometric spaces that are non-uniform with respect to the parallel postulate, since in a Riemannian manifold, the curvature may change from point to point. This corresponds roughly with what we will call semi-paradoxist. It would seem, therefore, that a study of Smarandache geometry should start...
In this paper, we study b−Smarandache m1m2 curves of biharmonic new type b−slant helix in the Sol3. We characterize the b−Smarandache m1m2 curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric equations in the Sol3.
Smarandache Geometries and Curves
by Esra Betul Koc Ozturk; Ufuk Ozturk; Kazim Ilarslan; Emilija Nesovic
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In this paper we define nonnull and null pseudospherical Smarandache curves according to the Sabban frame of a spacelike curve lying on pseudosphere in Minkowski 3-space. We obtain the geodesic curvature and the expressions for the Sabban frame’s vectors of spacelike and timelike pseudospherical Smarandache curves. We also prove that if the pseudospherical null straight lines are the Smarandache curves of a spacelike pseudospherical curve 𝛼, then 𝛼 has constant geodesic curvature....
Smarandache Geometries and Curves
by M. Elzawy; S. Mosa
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In this paper, we study Smarandache curves in the 4-dimensional Galilean space G4. We obtain Frenet Serret invariants for the Smarandache curve in G4. The first, second and third curvature of Smarandache curve are calculated. These values depending upon the first, second and third curvature of the given curve. Examples will be illustrated.
Smarandache Geometries and Curves
by Linfan Mao
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A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This monograph concentrates on characterizing various multi-spaces including three parts altogether. The first part is on algebraic multi-spaces with structures, such as those of multi-groups, multirings, multi-vector spaces, multi-metric spaces,...
Smarandache Geometries and Curves
by A. Nellai Murugan; P. Iyadurai Selvaraj
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A graph G is a finite non-empty set of objects called vertices together with a set of unordered pairs of distinct vertices of G which is called edges.
Smarandache Geometries and Curves
by Suleyman Senyurt; Abdussamet Caliskan; Unzile Celik
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In this paper, let (α, α∗) be Bertrand curve pair, when the unit Darboux vector of the α∗ curve are taken as the position vectors, the curvature and the torsion of Smarandache curve are calculated. These values are expressed depending upon the α curve. Besides, we illustrate example of our main results.
Smarandache Geometries and Curves
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In this paper, we introduce some special Smarandache curves according to Bishop frame in Euclidean 3-space E3. Also, we study Frenet-Serret invariants of a special case in E3. Finally, we give an example to illustrate these curves.
Smarandache Geometries and Curves
by Vahide Bulut; Ali Caliskan
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In this study, we introduce the spherical images of some special Smarandache curves according to Frenet frame and Darboux frame in E3. Besides, we give some differential geometric properties of Smarandache curves and their spherical images.
Smarandache Geometries and Curves
by R. Ponraj; M. Maria Adaickalam
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In this paper we investigate 3-difference cordial labeling behavior of DTn ⊙ K1 DTn ⊙ 2K1,DTn ⊙ K2 and some more graphs.
Smarandache Geometries and Curves
by Tanju Kahraman; Hasan Huseyin Ugurlu
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In this paper, we consider the notion of the Smarandache curves by considering the asymptotic orthonormal frames of curves lying fully on lightlike cone in Minkowski 3-space R. We give the relationships between Smarandache curves and curves lying on lightlike cone in R.
Smarandache Geometries and Curves
by R. Ponraj; Rajpal Singh; R. Kala
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In this paper we investigate 4-prime cordial labeling behavior of shadow graph of a path, cycle, star, degree splitting graph of a bistar, jelly fish, splitting graph of a path and star.
Smarandache Geometries and Curves
by Nurten Bayrak Gurses; Ozcan Bektas; Salim Yuce
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In this study, we determine TN-Smarandache curves whose position vector is composed by Frenet frame vectors of another regular curve in Minkowski 3-space R. Then, we present some characterisations of Smarandache curves and calculate Frenet invariants of these curves. Moreover, we classify TN; TB; NB and TNB-Smarandache curves of a regular curve parametrized by arc length by presenting a brief table with respect to the causal character. Also, we will give some examples related to results. In...
Smarandache Geometries and Curves
by Akram Alqesmah; Anwar Alwardi; R. Rangarajan
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In this paper, we introduce the first and second distance eccentricity Zagreb indices of a connected graph G as the sum of the squares of the distance eccentricity degrees of the vertices, and the sum of the products of the distance eccentricity degrees of pairs of adjacent vertices, respectively. Exact values for some families of graphs and graph operations are obtained.
Smarandache Geometries and Curves
by F. Smarandache
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In this article we present the two classical negations of Euclid’s Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry.
Smarandache Geometries and Curves
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In this paper we prove that ladder and subdivision of ladder are (1, N)-arithmetic labelling for every positive integer N > 1.
Smarandache Geometries and Curves
by Tanju Kahraman; Mehmet Önder; H. Huseyin Ugurlu
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In this paper, by considering dual geodesic trihedron (dual Darboux frame) we define dual Smarandache curves lying fully on dual unit sphere and corresponding to ruled surfaces. We obtain the relationships between the elements of curvature of dual spherical curve (ruled surface) and its dual Smarandache curve (Smarandache ruled surface) and we give an example for dual Smarandache curves of a dual spherical curve.
Smarandache Geometries and Curves
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In the present paper, we investigate special Smarandache curves with Darboux apparatus with respect to Frenet and Darboux frame of an arbitrary curve on a surface in the three-dimensional Galilean space G3. Furthermore, we give general position vectors of special Smarandache curves of geodesic, asymptotic and curvature line on the surface in G3. As a result of this, we provide some related examples of these curves.
Smarandache Geometries and Curves
by Esra Betul Koc Ozturk; Ufuk Ozturk; Kazim Ilarslan; Emilija Nesovic
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We define pseudohyperbolical Smarandache curves according to the Sabban frame in Minkowski 3-space.We obtain the geodesic curvatures and the expression for the Sabban frame vectors of special pseudohyperbolic Smarandache curves. Finally, we give some examples of such curves.
Smarandache Geometries and Curves
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The purpose of this paper is to study Smarandache curves in the 4-dimensional Euclidean space E4, and to obtain the Frenet–Serret and Bishop invariants for the Smarandache curves in E4. The first, the second and the third curvatures of Smarandache curves are calculated. These values depending upon the first, the second and the third curvature of the given curve.
Smarandache Geometries and Curves
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In this paper, we extend the study of Nk-index of a graph for other graph operations. Exact formulas of the Nk-index for corona G ◦ H and neighborhood corona G ⋆ H products of connected graphs G and H are presented. An explicit formula for the splitting graph S(G) of a graph G is computed. Also, the Nk-index formula of the join G + H of two graphs G and H is presented. Finally, we generalize the Nk-index formula of the join for more than two graphs.
Smarandache Geometries and Curves
by A. Lourdusamy; Sherry George
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Our attempt in this paper is to show that all the linear cyclic snakes, including kC4, are also super vertex mean graphs, even though C4 is not an SVM graph. We also define the term Super Vertex Mean number of graphs.
Smarandache Geometries and Curves
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In this study, we introduce new Smarandache curves of a spacelike curve according to the Bishop frame of type-2 in E31. Also, Smarandache breadth curves are defined according to this frame in Minkowski 3-space. A third order vectorial differential equation of position vector of Smarandache breadth curves has been obtained in Minkowski 3-space.
In this paper, we define Smarandache curves of null quaternionic curves in the semi-Euclidean space and obtain that curvatures of null quaternionic curves have some relations for Smarandache curves.
Smarandache Geometries and Curves
by U. M. Prajapati; R. M. Gajjar
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We discuss cordial labeling of graphs obtained from duplication of certain graph elements in web and armed helm.
Smarandache Geometries and Curves
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In my book Smarandache Manifolds, it is shown that the s-sphere has both closed and open s-lines. It is shown here that this is true for any closed s-manifold. This would make each closed s-manifold a Smarandache geometry relative to the axiom requiring each line to be extendable to infinity, since each closed s-line would have finite length. Furthermore, it is shown that whether a particular s-line is closed or not is determined locally, and it is determined precisely which s-lines are closed...
Smarandache Geometries and Curves
by T. Chalapathi; R. Kiran Kumar
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This paper introduces equal degree graphs of simple existed graphs. These graphs exhibited some properties which are co-related with the older one. We characterize graphs for which their equal degree graphs are connected, completed, disconnected but not totally disconnected. We also obtain several properties of equal degree graphs and specify which graphs are isomorphic to equal degree graphs and complement of equal degree graphs. Furthermore, the relation between equal degree graphs and degree...
Smarandache Geometries and Curves
by B. Basavanagoud; Sujata Timmanaikar
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In this paper, we initiate a study of this new parameter and obtain some results concerning this parameter.
Smarandache Geometries and Curves
by V. Lokesha; P. S. Hemavathi; S. Vijay
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In this paper we introduced the new notions semifull signed graph and semifull line (block) signed graph of a signed graph and its properties are obtained. Also, we obtained the structural characterizations of these notions. Further, we presented some switching equivalent characterizations.
Smarandache Geometries and Curves
by Süleyman Şenyurt; Yasin Altun; Ceyda Cevahir; Hüseyin Kocayiğit
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In this article, we investigate special Smarandache curves with regard to Sabban frame of involute curve. We created Sabban frame belonging to spherical indicatrix of involute curve. It was explained Smarandache curves position vector is consisted by Sabban vectors belonging to spherical indicatrix. Then, we calculated geodesic curvatures of this Smarandache curves. The results found for each curve was given depend on evolute curve. The example related to the subject were given and their...
Smarandache Geometries and Curves
by Ahmad T. Ali; Hossam S. Abdel Aziz; Adel H. Sorour
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In this paper, a family of ruled surfaces generated by some special curves using a Frenet frame of that curves in Euclidean 3-space is investigated. Some important results are obtained in the case of general helices as well as slant helices. Moreover, as an application, circular general helices, spherical general helices, Salkowski curves and circular slant helices, which illustrate the results, are provided and graphed.
Smarandache Geometries and Curves
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A paradoxist Smarandache geometry combines Euclidean, hyperbolic, and elliptic geometry into one space along with other non-Euclidean behaviors of lines that would seem to require a discrete space. A class of continuous spaces is presented here together with specific examples that exhibit almost all of these phenomena and suggest the prospect of a continuous paradoxist geometry.
Smarandache Geometries and Curves
by Elham Mehdi-Nezhad; Amir M. Rahimi
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Let R be a commutative ring with identity 1 ̸= 0. Define the comaximal graph of R, denoted by CG(R), to be the graph whose vertices are the elements of R, where two distinct vertices a and b are adjacent if and only if Ra + Rb = R. A vertex a in a simple graph G is said to be a Smarandache vertex (or S-vertex for short) provided that there exist three distinct vertices x, y, and b (all different from a) in G such that a—x, a—b, and b—y are edges in G but there is no edge between x and y....
Smarandache Geometries and Curves
by Roberto Torretti
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The Smarandache anti-geometry is a non-euclidean geometry that denies all Hilbert’s 20 axioms, each axiom being denied in many ways in the same space.
Smarandache Geometries and Curves
by K. Praveena; M. Venkatachalam
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An equitable k-coloring of a graph G is a proper k-coloring of G such that the sizes of any two color class differ by at most one. In this paper we investigate the equitable chromatic number for the Central graph, Middle graph, Total graph and Line graph of Triple star graph.
Smarandache Geometries and Curves
by Rajendra P.; R. Rangarajan
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Recently, Adiga, et.al. introduced, the minimum covering energy Ec(G) of a graph and S. Burcu Bozkurt, et.al. introduced, Randic Matrix and Randic Energy of a graph. Motivated by these papers, Minimum equitable dominating Randi´c energy of a graph REED(G) of some graphs are worked aut and bounds on REED(G) are obtained.
Smarandache Geometries and Curves
by Suleyman Senyurt; Abdussamet Caliskan
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In this paper, when the unit Darboux vector of the partner curve of Mannheim curve are taken as the position vectors, the curvature and the torsion of Smarandache curve are calculated. These values are expressed depending upon the Mannheim curve. Besides, we illustrate example of our main results.
This paper attempts to answear to Kuciuk and Antholy’s question if there is a general model for all Smarandache Geometries in such a way that replacing some parameters one gets any of the desired particular SG.
Smarandache Geometries and Curves
by M. H. Akhbari; F. Movahedi; S. V. R. Kulli
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In this paper, we obtain the domination number, the total domination number and the independent domination number in the neighborhood graph. We also investigate these parameters of domination on the join and the corona of two neighborhood graphs.
Smarandache Geometries and Curves
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In this paper we initiate a study on this parameter. In addition, we discuss the related problem of finding the stability of γetc upon edge addition on some classes of graphs.
Smarandache Geometries and Curves
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A regular curve in complex space, whose position vector is composed by Cartan frame vectors on another regular curve, is called a isotropic Smarandache curve. In this paper, I examine isotropic Smarandache curve according to Cartan frame in Complex 3-space and give some differential geometric properties of Smarandache curves.
Smarandache Geometries and Curves
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In this paper, we study Smarandache curves according to Darboux frame in the three-dimensional Minkowski space . Using the usual transformation between Frenet and Darboux frames, we investigate some special Smarandache curves for a given timelike curve lying fully on a timelike surface. Finally, we defray a computational example to confirm our main results.
Smarandache Geometries and Curves
by P. S. K. Reddy; K. N. Prakasha; Gavirangaiah K.
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In this paper, we introduce the minimum equitable dominating Randic energy of a graph and computed the minimum dominating Randic energy of graph. Also, established the upper and lower bounds for the minimum equitable dominating Randic energy of a graph.
Smarandache Geometries and Curves
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The Smarandache anti-geometry is a non-euclidean geometry that denies all Hilbert’s twenty axioms, each axiom being denied in many ways in the same space. In this paper one finds an economics model to this geometry by making the following correlations: (i) A point is the balance in a particular checking account, expressed in U.S. currency. (Points are denoted by capital letters). (ii) A line is a person, who can be a human being. (Lines are denoted by lower case italics). (iii) A plane is a...
Smarandache Geometries and Curves
by R. Ponraj; K. Annathurai
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In this paper we investigate the 4- remainder cordial behavior of grid, subdivision of crown, Subdivision of bistar, book, Jelly fish, subdivision of Jelly fish, Mongolian tent graphs.
Smarandache Geometries and Curves
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In this paper, we introduce special equiform Smarandache curves reference to the equiform Frenet frame of a curve ζ on a spacelike surface M in Minkowski 3-space E3. Also, we study the equiform Frenet invariants of the spacial equiform Smarandache curves in E3. Moreover, we give some properties to these curves when the curve ζ has constant curvature or it is a circular helix. Finally, we give an example to illustrate these curves.
In this paper, we investigate Smarandache curves according to type-2 Bishop frame in Euclidean 3- space and we give some differential geometric properties of Smarandache curves. Also, some characterizations of Smarandache breadth curves in Euclidean 3-space are presented. Besides, we illustrate examples of our results.
Smarandache Geometries and Curves
by Suleyman Senyurt; Abdussamet Caliskan
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In this paper, we investigate special Smarandache curves in terms of Sabban frame of spherical indicatrix curves and we give some characterization of Smarandache curves. Besides, we illustrate examples of our results.
Smarandache Geometries and Curves
by M. Khalifa Saad; R. A. Abdel-Baky
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This paper aims to study the skew ruled surfaces by using the quasi-frame of Smarandache curves in the Euclidean 3-space. Also, we reveal the relationship between SerretFrenet and quasi-frames and give a parametric representation of a directional ruled surface using the quasi-frame. Besides, some comparative examples are given and plotted which support our method and main results.
Smarandache Geometries and Curves
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In this paper, we analyzed surfaces family possessing a Mannheim partner curve of a given curve as a geodesic. Using the Frenet frame of the curve in Euclidean 3-space, we express the family of surfaces as a linear combination of the components of this frame and derive the necessary and sufficient conditions for coefficients to satisfy both the geodesic and isoparametric requirements. The extension to ruled surfaces is also outlined. Finally, examples are given to show the family of surfaces...
A complex system S consists m components, maybe inconsistence with m ≥ 2, such as those of biological systems or generally, interaction systems and usually, a system with contradictions, which implies that there are no a mathematical subfield applicable.
Smarandache Geometries and Curves
by T. Deepa; M. Venkatachalam
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Graphs in this paper are simple and finite. Thus for a graph G, δ(G), ∆(G) and χ(G) denote the minimum degree, maximum degree and chromatic number of G respectively.
Smarandache Geometries and Curves
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In this paper, we acquaint a special timelike Smarandache curves Z reference the Darboux frame of a timelike curve in Minkowski 3-space.
Smarandache Geometries and Curves
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As it is well-known, the geometry of curve in three-dimensions is actually characterized by Frenet vectors. In this paper, we obtain Smarandache curves by using cone frame formulas in null cone Q3. Also, we give an example related to these curves.