rainbow neighbourhood
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2020 ◽  
Vol 51 ◽  
Author(s):  
Johan Kok ◽  
Sudev Naduvath ◽  
Eunice Gogo Mphako-Banda


2019 ◽  
Vol 11 (2) ◽  
pp. 159-173
Author(s):  
Federico Fornasiero ◽  
Sudev Naduvath

Abstract A vertex v of a given graph G is said to be in a rainbow neighbourhood of G, with respect to a proper coloring C of G, if the closed neighbourhood N[v] of the vertex v consists of at least one vertex from every color class of G with respect to C. A maximal proper coloring of a graph G is a J-coloring of G such that every vertex of G belongs to a rainbow neighbourhood of G. In this paper, we study certain parameters related to J-coloring of certain Mycielski-type graphs.



2019 ◽  
Vol 38 (3) ◽  
pp. 469-484 ◽  
Author(s):  
Johan Kok ◽  
Sudev Naduvath ◽  
Muhammad Kamran Jamil


2019 ◽  
Vol 11 (1) ◽  
pp. 95-108
Author(s):  
Sudev Naduvath ◽  
Johan Kok

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.



2019 ◽  
Vol 31 (6) ◽  
Author(s):  
N.K. Sudev ◽  
C. Susanth ◽  
S.J. Kalayathankal


2018 ◽  
Vol 42 (3) ◽  
pp. 249-252
Author(s):  
Sudev Naduvath ◽  
Susanth Chandoor ◽  
Sunny Joseph Kalayathankal ◽  
Johan Kok


2018 ◽  
Vol 42 (2) ◽  
pp. 135-138
Author(s):  
Sudev Naduvath ◽  
Susanth Chandoor ◽  
Sunny Joseph Kalayathankal ◽  
Johan Kok


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