Dominating Cocoloring of Graphs
M. Poobalaranjani1, R.Pichailakshm2
1M.Poobalaranjani*, PG & Research Department of Mathematics Seethalakshmi Ramaswami College, Tiruchirappalli, Tamil Nadu, India.
2R.Pichailakshmi, PG & Research Department of Mathematics Seethalakshmi Ramaswami College, Tiruchirappalli, Tamil Nadu, India.
Manuscript received on October 12, 2019. | Revised Manuscript received on 22 October, 2019. | Manuscript published on November 10, 2019. | PP: 2545-2547 | Volume-9 Issue-1, November 2019. | Retrieval Number: A4990119119/2019©BEIESP | DOI: 10.35940/ijitee.A4990.119119
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Abstract: A -cocolouring of a graph is a partition of the vertex set into subsets such that each set induces either a clique or an independent set in . The cochromatic number of a graph is the least such that has a -cocolouring of . A set is a dominating set of if for each , there exists a vertex such that is adjacent to . The minimum cardinality of a dominating set in is called the domination number and is denoted by . Combining these two concepts we have introduces two new types of cocoloring viz, dominating cocoloring and -cocoloring. A dominating cocoloring of is a cocoloring of such that atleast one of the sets in the partition is a dominating set. Hence dominating cocoloring is a conditional cocoloring. The dominating co-chromatic number is the smallest cardinality of a dominating cocoloring of .(ie) has a dominating cocoloring with -colors .
Keywords: Colouring, Cochromatic Number, Dominating Cocoloring, Dominating Cochromatic Number, Dominating Cocolorable Graphs.
Scope of the Article: Graph Algorithms and Graph Drawing