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National Academy Science Letters

, Volume 42, Issue 2, pp 135–138 | Cite as

A Note on the Rainbow Neighbourhood Number of Certain Graph Classes

  • Sudev NaduvathEmail author
  • Susanth Chandoor
  • Sunny Joseph Kalayathankal
  • Johan Kok
Short Communication
  • 26 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 colored vertex of each color in the chromatic coloring \({\mathscr {C}}\) of G. Let G be a graph with a chromatic coloring \({\mathscr {C}}\) defined on it. The number of vertices in G yielding rainbow neighbourhoods is called the rainbow neighbourhood number of the graph G, denoted by \(r_\chi (G)\). In this paper, rainbow neighbourhood number of certain graph classes are discussed.

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.Centre for Studies in Discrete MathematicsVidya Academy of Science and Technology ThalakkottukaraThrissurIndia

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