Enumerating the number of spanning trees and the Asymptotic Behavior of Some Wheel Related Graphs

Abstract

Wheel graphs are fundamental structures in graph theory and network architectures. Their importance arises mostly from the fact that they are planar, self-dual graphs used to mimic central hub-and-spoke networks, such as transportation and communication systems, and to study network fragility, symmetry, and chromatic characteristics. In this study, we derive explicit formulas for the number of spanning trees of new classes of wheel related graph families using linear algebraic methods and the properties of Chebyshev polynomials. The asymptotic entropy of the spanning trees in our graphs was also examined. Finally, we contrast the entropies of our graphs with those of other graphs that have been previously examined and have an average of four or five degrees.