Open AccessDominating Cocoloring of Graphs
Author(s) -
M Poobalaranjani,
R. Pichailakshmi
Publication year - 2019
Publication title -
international journal of innovative technology and exploring engineering
Language(s) - English
Resource type - Journals
ISSN - 2278-3075
DOI - 10.35940/ijitee.a4990.119119
Subject(s) - dominating set , combinatorics , mathematics , vertex (graph theory) , domination analysis , partition (number theory) , graph , discrete mathematics
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 .