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arXiv · 1410.7988

Tutte polynomial of a fractal scale-free lattice

Hanlin Chen·Yuanhua Liao·Hanyuan Deng
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Abstract

The Tutte polynomial of a graph, or equivalently the $q$-state Potts model partition function, is a two-variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. The computation of this invariant for a graph is NP-hard in general. In this paper, based on their self-similar structures, we recursively describe the Tutte polynomials of an infinite family of scale-free lattices. Furthermore, we give some exact analytical expressions of the Tutte polynomial for several special points at $(X,Y)$-plane.

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Hanlin Chen, Yuanhua Liao, Hanyuan Deng. 2014-10-29. Tutte polynomial of a fractal scale-free lattice. https://arxiv.org/abs/1410.7988

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