School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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

Comments

Under the Creative Commons Attribution-NonCommercial-NoDerivs license, the author(s) and users are free to share (copy, distribute and transmit the contribution) under the following conditions: 1. they must attribute the contribution in the manner specified by the author or licensor, 2. they may not use this contribution for commercial purposes, 3. they may not alter, transform, or build upon this work.

Publication Title

Discussiones Mathematicae Graph Theory

DOI

https://doi.org/10.7151/dmgt.2385

Included in

Mathematics Commons

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