Global Dominator Chromatic Number of Certain Graphs

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Nouri Samani Hadi; Alikhani Saeid; Ghanbari Nima

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Journal Paper

Paper Information

Journal: MATHEMATICS INTERDISCIPLINARY RESEARCH Year:2025 | Volume:10 | Issue:2 Page(s): 183-198

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Information Journal Paper

Title

Global Dominator Chromatic Number of Certain Graphs

Author(s)

Nouri Samani Hadi | Alikhani Saeid | Ghanbari Nima | Issue Writer Certificate

Keywords

Global domination‎

‎Global dominator coloring‎

‎Corona‎

‎Cactus‎

‎Cubic

Abstract

‎For a graph G=(V,E) and a vertex subset $D\subseteq V$‎, ‎a vertex $v\in V$ is called a dominator of D if v is adjacent to every vertex in D‎, ‎and an anti-dominator of D if v is not adjacent to any vertex in D. ‎Given a coloring $C=\{V_{1},V_{2},\ldots,V_{k}\}$ of $G$‎, ‎a color {class $V_{i}$} {is a dominating color class (resp. an anti dominating color class) for a vertex ‎v‎‎ if ‎‎v‎‎ dominates all vertices in ‎$‎V_i‎$‎ (resp. ‎‎v‎‎ dominates no vertex in ‎$‎V_i‎$‎)}‎. ‎A coloring C is a global dominator coloring if each vertex in $G$ has both a dominating and an anti-dominating color class‎. ‎The global dominator chromatic number‎, ‎denoted by $\chi_{gd}(G)$‎, ‎is the minimum number of colors required for a global dominator coloring of $G$‎. ‎In this paper‎, ‎we investigate the global dominator chromatic number for various classes of graphs‎.

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