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arXiv · 2311.06161

On irredundance coloring and irredundance compelling coloring of graphs

David Ashok Kalarkop·Pawaton Kaemawichanurat
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Abstract

Irredundance coloring of $G$ is a proper coloring in which there exists a maximal irredundant set $R$ such that all the vertices of $R$ have different colors. The minimum number of colors required for an irredundance coloring of $G$ is called the irredundance chromatic number of $G$, and is denoted by $\chi_{i}(G)$. Irredundance compelling coloring of $G$ is a proper coloring of $G$ in which every rainbow committee (the set containing a vertex of each color) is an irredundant set of $G$. The maximum number of colors required for an irredundance compelling coloring of $G$ is called the irredundance compelling chromatic number of $G$, and is denoted by $\chi_{irc}(G)$. In this paper, we make a detailed study on $\chi_{i}(G)$, $\chi_{irc}(G)$ and its relation to other coloring and domination parameters

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David Ashok Kalarkop, Pawaton Kaemawichanurat. 2023-11-10. On irredundance coloring and irredundance compelling coloring of graphs. https://arxiv.org/abs/2311.06161

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