R-Dynamic chromatic number of subdivision-edge neighborhood corona of certain graph families

Abstract

Let [Formula: see text] be a simple connected graph consisting of n vertices and m edges. In a proper [Formula: see text]-coloring, an [Formula: see text]-dynamic coloring of a graph [Formula: see text] is one in which each vertex’s neighbors are provided at least min [Formula: see text] different colors. The [Formula: see text]-dynamic chromatic number of graph [Formula: see text], given as [Formula: see text], is the minimal [Formula: see text] such that the graph has [Formula: see text]-dynamic [Formula: see text] coloring of [Formula: see text]. In this study, we combine a few common graphs to provide the [Formula: see text]-dynamic coloring of the subdivision-edge neighborhood corona of path graph [Formula: see text] and star graph [Formula: see text]. These graphs include path graph [Formula: see text], cycle graph [Formula: see text], complete graph [Formula: see text], star graph [Formula: see text], and double star graph [Formula: see text].