<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

J-coloring of graph operations

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"J-coloring of graph operations"}

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...

J-coloring of graph operations

Published Online: Aug 21, 2019

Page range: 95 - 108

Received: Jul 04, 2019

DOI: https://doi.org/10.2478/ausi-2019-0007

Keywords
rainbow neighbourhood, J-coloring, J*-coloring

© 2019 Sudev Naduvath et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

J-coloring of graph operations

Published Online: Aug 21, 2019

Page range: 95 - 108

Received: Jul 04, 2019

DOI: https://doi.org/10.2478/ausi-2019-0007

Keywordsrainbow neighbourhood, J-coloring, J*-coloring

© 2019 Sudev Naduvath et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
rainbow neighbourhood, J-coloring, J*-coloring