Dominated chromatic number of some operations on a graph

Let $G$ be a simple graph. The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $\chi_{dom}(G)$...

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Bibliographic Details
Main Authors Alikhani, Saeid, Piri, Mohammad R
Format Journal Article
LanguageEnglish
Published 29.11.2019
Subjects
Mathematics - Combinatorics
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Summary:Let $G$ be a simple graph. The dominated coloring of a graph $G$ is a proper coloring of $G$ such that each color class is dominated by at least one vertex. The minimum number of colors needed for a dominated coloring of $G$ is called the dominated chromatic number of $G$, denoted by $\chi_{dom}(G)$. In this paper, we examine the effects on $\chi_{dom}(G)$ when $G$ is modified by operations on vertex and edge of $G$.
DOI:10.48550/arxiv.1912.00016