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Dominating Cocoloring of Graphs
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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 .
Blue Eyes Intelligence Engineering and Sciences Engineering and Sciences Publication - BEIESP
Title: Dominating Cocoloring of Graphs
Description:
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 .
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