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Rainbow Domination in Graphs

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Topics in Domination in Graphs

Part of the book series: Developments in Mathematics ((DEVM,volume 64))

Abstract

A function f, which assigns to each vertex of a graph G a subset of the color set {1, …, k}, is called a k-rainbow dominating function of G if for each v ∈ V (G) with f(v) = ∅ all k colors appear in the neighborhood of v. The weight of f is the sum of |f(v)| over all vertices v in G, and the minimum weight of a k-rainbow dominating function of G is called the k-rainbow domination number, γ rk(G), of G. Equivalently, the k-rainbow domination number of a graph G is the domination number of the Cartesian product of G with the complete graph K k. In this chapter, we survey main results on rainbow domination and related concepts in graphs.

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Acknowledgements

The author was in part supported by the Slovenian Research Agency (ARRS) under the grants P1-0297 and J1-9109.

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Authors and Affiliations

  1. Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia

    Boštjan Brešar

  2. Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia

    Boštjan Brešar

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Editors and Affiliations

  1. Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN, USA

    Teresa W. Haynes

  2. School of Computing, Clemson University, Clemson, SC, USA

    Stephen T. Hedetniemi

  3. Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa

    Michael A. Henning

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Brešar, B. (2020). Rainbow Domination in Graphs. In: Haynes, T.W., Hedetniemi, S.T., Henning, M.A. (eds) Topics in Domination in Graphs. Developments in Mathematics, vol 64. Springer, Cham. https://doi.org/10.1007/978-3-030-51117-3_12

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