Title

Burnside chromatic polynomials of group-invariant graphs

Document Type

Article

Publication Date

6-17-2020

Abstract

We introduce the Burnside chromatic polynomial of a graph that is invariant under a group action. This is a generalization of the Q-chromatic function Zaslavsky introduced for gain graphs. Given a group G acting on a graph G and a G-set X, a proper X-coloring is a function with no monochromatic edge orbit. The set of proper colorings is a G-set which induces a polynomial function from the Burnside ring of G to itself. In this paper, we study many properties of the Burnside chromatic polynomial, answering some questions of Zaslavsky

Publication Title

Discussiones Mathematicae Graph Theory

DOI

10.7151/dmgt.2385

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