The Tutte symmetric matrix of a graph
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912986597163008 |
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| author | Tom, Foster Vailaya, Aarush |
| author_facet | Tom, Foster Vailaya, Aarush |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27129 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Tutte symmetric matrix of a graph Tom, Foster Vailaya, Aarush Combinatorics 05C50, 05E05, 05C15 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). |
| title | The Tutte symmetric matrix of a graph |
| topic | Combinatorics 05C50, 05E05, 05C15 |
| url | https://arxiv.org/abs/2603.27129 |