Title: Critical injective chromatic graphs

Authors: Anjaly Kishore; M.S. Sunitha

Addresses: Department of Mathematics, Vimala College, Thrissur, Kerala, India ' Department of Mathematics, National Institute of Technology Calicut, Kozhikode, Kerala, India

Abstract: The concept of critical injective chromatic graph is introduced. Some properties of critical injective chromatic graph are studied based on number of vertices and degree of graphs. The condition for cycles to be critical injective chromatic is obtained. The existence of a critical injective chromatic graph is established. An algorithm for injective colouring of vertices of a given connected graph is proposed. An application of injective chromatic number and injective chromatic sum in the diagnosis of diseases based on symptoms is suggested.

Keywords: injective chromatic number; chromatic sum; cycles; paths; critical injective chromatic graph; algorithm; disease diagnosis.

DOI: 10.1504/IJCSM.2017.088014

International Journal of Computing Science and Mathematics, 2017 Vol.8 No.5, pp.457 - 464

Accepted: 08 May 2017
Published online: 14 Nov 2017 *

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