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arXiv · 2603.27129

The Tutte symmetric matrix of a graph

Foster Tom·Aarush Vailaya
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Abstract

We provide a matrix-based formula for the Tutte symmetric function of a graph. In particular, for any graph $G$ with a designated head and tail vertex, we describe an infinite matrix $M_G$ from which the Tutte symmetric function can be easily recovered. We prove gluing graphs together corresponds to matrix multiplication, gluing the head and tail of a single graph corresponds to taking the trace, and reversing a graph corresponds to the transpose (up to a change of basis).

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Foster Tom, Aarush Vailaya. 2026-03-28. The Tutte symmetric matrix of a graph. https://arxiv.org/abs/2603.27129

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