The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs

Tutte Polynomial of Scale-Free Networks

“…Recently, on the basis of the subgraph expansion definition of the Tutte polynomial, a very useful method for computing the Tutte polynomial, called the subgraphdecomposition method, was developed by Donno et al [18]. This technique is highly suited for computing the Tutte polynomial of self-similar graphs, and some applications of it can be found in [19,20,21].…”

Tutte polynomial of the Apollonian network

“…Recently, on the basis of the subgraph expansion definition of the Tutte polynomial, a very useful method for computing the Tutte polynomial, called the subgraph-decomposition method, was developed by Donno et al [18]. This technique is highly suited to computing the Tutte polynomial of self-similar graphs and some applications of it can be found in [19][20][21].…”

“…In this work we focus our attention on the computation of the Tutte polynomial of the Apollonian network. Unlike the Sierpinski gasket [18], the Farey graph [19] and other self-similar graphs [20,21], it is very complicated for us to apply the subgraphdecomposition method directly on the Apollonian network. Motivated by Zhang et al [33] who enumerated the number of spanning trees of the Apollonian network through enumerating those of the Apollonian dual graph, here we propose a less direct approach which is, nevertheless, capable of computing the Tutte polynomial of the Apollonian network.…”