Abstract

A vertex v of a given graph is said to be in a rainbow neighbourhood of G if every color class of G consists of at least one vertex from the closed neighbourhood N[v]. A maximal proper coloring of a graph G is a J-coloring if and only if every vertex of G belongs to a rainbow neighbourhood of G. In general all graphs need not have a J-coloring, even though they admit a chromatic coloring. In this paper, we characterise graphs which admit a J-coloring. We also discuss some preliminary results in respect of certain graph operations which admit a J-coloring under certain conditions.

Details

Title
J-coloring of graph operations
Author
Naduvath, Sudev 1 ; Kok, Johan 2 

 Department of Mathematics, CHRIST (Deemed to be University, Bangalore, India 
 Department of Mathematics, CHRIST (Deemed to be UniversityBangalore, India 
Pages
95-108
Publication year
2019
Publication date
2019
Publisher
De Gruyter Poland
ISSN
18446086
e-ISSN
20667760
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
3156003966
Copyright
© 2019. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.