Computing the number of spanning trees in the Wheel multiple graph

Abstract

The number of spanning trees in a network relevant to several networks aspects, namely their topological and dynamic properties such as their reliability. Generally, this number can be obtained by the well-known Matrix Tree Theorem. However, computing the number of spanning trees in a network using this method is computationally demanding specially for a large network, which leads us to investigate the number of spanning trees in planar graphs. In this paper, we propose an efficient method to find exact formulas for counting the number of spanning trees in a general type of the multiple planar wheel graph.