R-Chromatic Number On r-Dynamic Vertex Coloring of Comb Graph

Abstract

Let be a graph with vertex set and edge set . An r-dynamic vertex coloring of a graph is a assigning colors to the vertices of such that for every vertex receives at least colors in its neighbors. The minimum color used in r-dynamic vertex coloring of graph is called the r-dynamic chromatic number denoted as . In this research we well determine the coloring pattern and the r-dynamic chromatic number of the comb graph , central graph of comb graph , middle graph of comb graph , line graph of comb graph , sub-division graf of comb graph , and para-line graph of comb graph Let be a graph with vertex set and edge set . An r-dynamic vertex coloring of a graph is a assigning colors to the vertices of such that for every vertex receives at least colors in its neighbors. The minimum color used in r-dynamic vertex coloring of graph is called the r-dynamic chromatic number denoted as . In this research we well determine the coloring pattern and the r-dynamic chromatic number of the comb graph , central graph of comb graph , middle graph of comb graph , line graph of comb graph , sub-division graf of comb graph , and para-line graph of comb graph