On r-dynamic vertex coloring of some flower graph families

Abstract

e a simple, connected undirected graph with m vertices and n edges. Let ver tex coloring c of a graph G be a mapping c : V (G) → S, where |S| = k and it is k-colorable. Vertex coloring is proper if none of the any two neighboring vertices receives the similar color. An r-dynamic coloring is a proper coloring such that |c(Nbd(v))| ≥ min{r, degG(v)}, for each v ∈ V (G). The r-dynamic chromatic number of a graph G is the minutest coloring k of G which is r-dynamic k-colorable and denoted by χr(G). By a simple view, we exhibit that χr(G) ≤ χr+1(G), howbeit χr+1(G) − χr(G) cannot be arbitrarily small. Thus, finding the result of χr(G) is useful. This study gave the result of r-dynamic chromatic number for the central graph, Line graph, Subdivision graph, Line of subdivision graph, Splitting graph and Mycielski graph of the Flower graph Fn denoted by C(Fn), L(Fn), S(Fn), L(S(Fn)), S(Fn) and μ(Fn), respectively.