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A Note on the Rainbow Neighbourhood Number of Certain Graph Classes

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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.

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Authors and Affiliations

  1. Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, Karnataka, 560029, India

    Sudev Naduvath

  2. Department of Mathematics, Research and Development Centre, Bharathiar University, Coimbatore, Tamil Nadu, 641046, India

    Susanth Chandoor

  3. Department of Mathematics, Kuriakose Elias College, Mannanam, Kottayam, Kerala, 686561, India

    Sunny Joseph Kalayathankal

  4. Centre for Studies in Discrete Mathematics, Vidya Academy of Science and Technology Thalakkottukara, Thrissur, 680501, Kerala, India

    Johan Kok

Authors
  1. Sudev Naduvath
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  2. Susanth Chandoor
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  3. Sunny Joseph Kalayathankal
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  4. Johan Kok
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Correspondence to Sudev Naduvath.

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Naduvath, S., Chandoor, S., Kalayathankal, S.J. et al. A Note on the Rainbow Neighbourhood Number of Certain Graph Classes. Natl. Acad. Sci. Lett. 42, 135–138 (2019). https://doi.org/10.1007/s40009-018-0702-6

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  • DOI: https://doi.org/10.1007/s40009-018-0702-6

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