Title: Dominator chromatic number of m-Splitting graph and m-Shadow graph of path graph

Authors: T. Manjula; R. Rajeswari

Addresses: Sathyabama Institute of Science and Technology (Deemed to be University), Chennai, India ' Sathyabama Institute of Science and Technology (Deemed to be University), Chennai, India

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.

Keywords: domination; colouring; dominator colouring; m-Splitting graph; m-Shadow graph; path graph.

DOI: 10.1504/IJBET.2018.093089

International Journal of Biomedical Engineering and Technology, 2018 Vol.27 No.1/2, pp.100 - 113

Received: 30 Mar 2017
Accepted: 21 Jul 2017
Published online: 09 Jul 2018 *

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