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National Academy Science Letters

, Volume 42, Issue 3, pp 249–252 | Cite as

Some New Results on the Rainbow Neighbourhood Number of Graphs

  • Sudev NaduvathEmail author
  • Susanth Chandoor
  • Sunny Joseph Kalayathankal
  • Johan Kok
Short Communication
  • 30 Downloads

Abstract

A rainbow neighbourhood of a graph G is the closed neighbourhood N[v] of a vertex \(v \in V(G)\) which contains at least one coloured vertex of each colour in the chromatic colouring \({\mathscr {C}}\) of G. Let G be a graph with a chromatic colouring \({\mathscr {C}}\) defined on it. The number of vertices in G yielding rainbow neighbourhoods is called the rainbow neighbourhood number of the graph G, denoted by \(r_\chi (G)\). Rainbow neighbourhood number of the complements and products of certain fundamental graph classes are discussed in this paper.

Keywords

Colour classes Rainbow neighbourhood Rainbow neighbourhood number 

Mathematics Subject Classification

05C15 05C75 

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Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.Department of MathematicsCHRIST (Deemed to be University)BengaluruIndia
  2. 2.Department of Mathematics, Research and Development CentreBharathiar UniversityCoimbatoreIndia
  3. 3.Department of MathematicsKuriakose Elias College MannanamKottayamIndia
  4. 4.Tshwane Metropolitan Police DepartmentCity of TshwaneSouth Africa

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