Autonomous exploration is a critical capability for robots deployed in real-world situations. Often, these robots are required to navigate environments with little or no prior knowledge in an efficient manner. We investigate an approach to such exploration that selects between candidate frontiers based on the expected information gain. The system uses entropy values of the area map as a measure of the change in overall information and employs established simultaneous localization and mapping (SLAM) techniques. An additional factor considered is the benefit from revisiting previously mapped areas to create loop closures to increase accuracy. We document the approach, including the measure of entropy and loop-closure method. The system is evaluated through simulations and experiments with a live robot. We also evaluate different values for the weighting factors of the utility function, biasing the behavior toward either exploration or relocation. The simulated experiments demonstrate improved efficiency and accuracy in exploring and mapping an unknown environment when compared against a nearest-frontier approach. Results from real-world implementation of the system on robotic platforms, as well as experiments varying the weighting factors of the utility function on the implemented system, are also presented.