Abstract
Graph theory techniques are applied to several biological domains. The application of graph colouring and domination in the field of biology and medicine includes identifying drug targets, determining the role of proteins, genes of unknown function. The area obtained by combining graph colouring and domination is called the dominator colouring of a graph. This is defined as proper colouring of vertices in which every vertex of the graph dominates all vertices of at least one colour class. The least number of colours required for a dominator colouring of a graph is called the dominator chromatic number. The dominator chromatic number and domination number are obtained for m-Splitting graph and m-Shadow graph of path graph and a relationship between them is expressed in this paper.
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