Dom-Color Number of a Graph

A.Muthukamatchi

doi:https://doi.org/10.14445/22315373/IJMTT-V44P536

International Journal of Mathematics Trends and Technology

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Volume 44 | Number 4 | Year 2017 | Article Id. IJMTT-V44P536 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P536

Dom-Color Number of a Graph

A.Muthukamatchi

Abstract

Let G be a graph with χ(G) = k.then G is called k-chromatic.In a coloring of G, the set of all vertices with a given color is called a color class. Let C = {V1,V2,...,Vk} be a k-coloring of G. Let dC denote the number of color classes in C which are dominating sets of G. Then dχ = max dC , where the maximum is taken over all k colorings of G , which we call the dom-color number of G. A partition of V into independent dominating sets of G is called an independent domatic partition of G or indomatic partition of G. A graph G which admits an independent domatic partition is called indominable. The maximum order of an independent domatic partition of G is called the indomatic number of G and is denoted by di(G). The chromatic bondage number ρ(G) is the minimum number of edges between two color classes in a k- coloring of G, where the minimum is taken over all k-colorings of G. We present several interesting results on dom-color number and chromatic bondage number .

Keywords

dom-color number , Chromatic bondage number, indomatic number

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Citation :

A.Muthukamatchi, "Dom-Color Number of a Graph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 4, pp. 260-262, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P536