Dom-Chromatic Number of Corona Product of Path with Cycle and Path Related Graphs

Abstract

Graph theory has emerged as an important field of study owing to its wide range of practical applications. A proper coloring of a graph  is an assignment of different colors to adjacent vertices and the minimum number of colors required is called the chromatic number denoted by . A set  is called a dominating set if each vertex in  has at least one neighbor in , the smallest possible size of such a set is represented by . By combining these two concepts, the notion of dom coloring was introduced. A dom coloring set(dc-set) is a dominating set if it includes a vertex from each color class. The minimum size of a dc-set is referred as the dom chromatic number and is symbolized by  In this study, we determine the dom chromatic number for the corona product of a path  with certain cycle and path related graphs namely wheel graph, gear graph, ladder graph, grid graphs.