Global dominating sets in minimum coloring. (English) Zbl 1298.05119
Summary: In this paper, we introduce the concept of global dominating-{\(\chi\)}-coloring of a graph and the corresponding parameter namely global dominating-{\(\chi\)}-color number. Let \(G\) be a graph. Among all {\(\chi\)}-colorings of \(G\), a coloring with the maximum number of color classes that are global dominating sets in \(G\) is called a global dominating-{\(\chi\)}-coloring of \(G\). The number of color classes that are global dominating sets in a global dominating-{\(\chi\)}-coloring of \(G\) is defined to be the global dominating-{\(\chi\)}-color number of \(G\), denoted by \(\mathrm{gd}\chi(G)\).
MSC:
| 05C15 | Coloring of graphs and hypergraphs |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
| 05C35 | Extremal problems in graph theory |
References:
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