Dominator Coloring of Central and Middle Graph of Closed Helm Graph

Abstract

Graph coloring and domination are the two fields of graph theory that have numerous applications in the field of computer science and biological networks. An area attained by merging the graph coloring and domination known as dominator coloring of a graph. It is well-defined as a proper coloring of vertices where each vertex of graph governs all vertices in an atleast 1 color class. The least number of colors is essential for a dominator coloring of a graph known as dominator chromatic number. The dominator chromatic number for central and middle graph of the closed Helm graph is obtained and a relationship between them is expressed in this paper.