Tutte polynomial of self-similar network models with applications

Abstract

Determining the Tutte polynomial T ( G ; x , y ) of a graph network G is a challenging problem for mathematicians, physicians, and statisticians. This paper investigates a self-similar network model M ( t ) and derives its Tutte polynomial. In addition, we evaluate exact explicit formulas for the number of acyclic orientations and spanning trees of it as applications of the Tutte polynomial. Finally, we use the derived T ( M ( t ) ; x , y ) to obtain the Tutte polynomial of another self-similar model N ( t ) presented in [1] and correct the main result discussed in [1] by Ma et al. and test our result numerically by using Matlab.