Global Dominator Chromatic Number of Certain Graphs
نویسندگان
1 Department of Mathematical Sciences, Yazd University, Yazd, Iran
2 Department of Mathematical Sciences, Yazd University, Yazd, Iran
3 Department of Mathematical Sciences, Yazd University, Yazd, Iran
doi
10.22052/mir.2025.255889.1487چکیده
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.
