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arXiv · 2007.11042

A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function

José Aliste-Prieto·Logan Crew·Sophie Spirkl·José Zamora
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Abstract

This paper has two main parts. First, we consider the Tutte symmetric function $XB$, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of $XB$ and show that this function admits a deletion-contraction relation. We also demonstrate that the vertex-weighted $XB$ admits spanning-tree and spanning-forest expansions generalizing those of the Tutte polynomial by connecting $XB$ to other graph functions. Second, we give several methods for constructing nonisomorphic graphs with equal chromatic and Tutte symmetric functions, and use them to provide specific examples.

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José Aliste-Prieto, Logan Crew, Sophie Spirkl, José Zamora. 2020-07-21. A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function. https://arxiv.org/abs/2007.11042

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