2017/04/03 by Johan Kok, Sudev Naduvath, Kok, Johan +1
Computer Science · Engineering · #05C15 #05C38 #05C75 #05C85 #Advanced Graph Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1704.02869
openalex publication_date 2017/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A vertex v of a given graph is said to be in a rainbow neighbourhood of G if every colour class of G consists of at least one vertex from the closed neighbourhood N[v]. A maximal proper colouring of a graph G is a Johan colouring if and only if every vertex of G belongs to a rainbow neighbourhood of G. In general all graphs need not have a Johan colouring, even though they admit a chromatic colouring. In this paper, we characterise graphs which admit a Johan colouring. We also discuss some preliminary results in respect of certain graph operations which admit a Johan colouring under certain conditions.