combinatorics

New relations for the vertex polynomial

arXiv:2607.27488

summary

The paper extends the vertex polynomial to graphs of any degree and establishes local relations that apply when a graph contains small cycles such as digons, triangles, quadrilaterals, or pentagons.

Abstract

We extend the vertex polynomial to graphs of arbitrary degree and prove local relations that hold when a graph contains a digon, triangle, quadrilateral or pentagon.

4 pages

Topics & keywords

#graph theory#vertex polynomial#graph invariants#cycle relations#combinatorial topologyvertex polynomialdigontrianglequadrilateralpentagonlocal relationsarbitrary-degree graphs