Burnside Chromatic Polynomials of Group-Invariant Graphs

IF 0.5 4区数学 Q3 MATHEMATICS

Discussiones Mathematicae Graph Theory Pub Date : 2022-11-25 DOI:10.7151/dmgt.2385

J. White

引用次数: 0

Abstract

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.

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群不变图的Burnside色多项式

摘要引入了一类图在群作用下不变的Burnside色多项式。这是Zaslavsky为增益图引入的q色函数的推广。给定一个作用于图G和𝕲-set X的群，适当的X着色是一个没有单色边缘轨道的函数。适当着色的集合是一个𝕲-set，它从的伯恩赛德环引出一个多项式函数。本文研究了Burnside色多项式的许多性质，回答了Zaslavsky的一些问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discussiones Mathematicae Graph Theory MATHEMATICS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

53 weeks

期刊介绍： The Discussiones Mathematicae Graph Theory publishes high-quality refereed original papers. Occasionally, very authoritative expository survey articles and notes of exceptional value can be published. The journal is mainly devoted to the following topics in Graph Theory: colourings, partitions (general colourings), hereditary properties, independence and domination, structures in graphs (sets, paths, cycles, etc.), local properties, products of graphs as well as graph algorithms related to these topics.