图的Domination染色

doi:10.12677/PM.2023.136183

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图的Domination染色
Domination Coloring of Graphs

DOI: 10.12677/PM.2023.136183, PDF, HTML, 下载: 178 浏览: 269
作者: 严旭东：青海师范大学数学与统计学院，青海西宁
关键词: Domination 染色；Domination 色数；操作图；Domination Coloring； Domination Chromatic Number； Operations of Graph

摘要: 图 G 的一个 Domination 染色是使得图 G 的每个顶点 v 控制至少一个色类(可能是自身的色类)，并且每一个色类至少被 G 中一个顶点控制的一个正常染色。图 G 的 Domination 色数是图 G 的 Domination 染色所需最小的颜色数目，用 χdd(G) 表示。本文研究了图 G 的 Domination 色数与图 G 通过某种操作得到图 G"的 Domination 色数之间的关系。

Abstract: A domination coloring of a graph G is such that each vertex v of graph G dominates at least one color class (possibly it's own color class), and each color class is dominated by at least one vertex in G. The minimum number of colors among all domination colorings is called the domination chromatic number, denoted by χdd(G). In this paper, we study the domination coloring of the graph G and G", where G" obtained through some operation of G.

文章引用：严旭东. 图的Domination染色[J]. 理论数学, 2023, 13(6): 1792-1800. https://doi.org/10.12677/PM.2023.136183

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