On r-dynamic vertex coloring of some flower graph families

Abstract

Let [Formula: see text] be a simple, connected undirected graph with [Formula: see text] vertices and [Formula: see text] edges. Let vertex coloring [Formula: see text] of a graph [Formula: see text] be a mapping [Formula: see text], where [Formula: see text] and it is [Formula: see text]-colorable. Vertex coloring is proper if none of the any two neighboring vertices receives the similar color. An [Formula: see text]-dynamic coloring is a proper coloring such that [Formula: see text] min[Formula: see text], for each [Formula: see text][Formula: see text]. The [Formula: see text]-dynamic chromatic number of a graph [Formula: see text] is the minutest coloring [Formula: see text] of [Formula: see text] which is [Formula: see text]-dynamic k-colorable and denoted by [Formula: see text]. By a simple view, we exhibit that [Formula: see text], howbeit [Formula: see text] cannot be arbitrarily small. Thus, finding the result of [Formula: see text] is useful. This study gave the result of [Formula: see text]-dynamic chromatic number for the central graph, Line graph, Subdivision graph, Line of subdivision graph, Splitting graph and Mycielski graph of the Flower graph [Formula: see text] denoted by [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] respectively.