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Broadcast Domination in Graphs

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Structures of Domination in Graphs

Part of the book series: Developments in Mathematics ((DEVM,volume 66))

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Abstract

For a graph G, a function f : V (G) →{0, 1, …, diam(G)} is a broadcast on G, where diam(G) denotes the diameter of G. For each vertex v in G, the value f(v) is the strength of the broadcast from v. For each vertex u ∈ V (G), if there exists a vertex v in G (possibly, u = v) such that f(v) > 0 and d(u, v) ≤ f(v), where d(u, v) is the distance betweenu and v, then f is called a dominating broadcast on G. The cost of the dominating broadcast f is the sum of the strengths of the broadcasts over all vertices in G, that is, the quantity ∑v ∈ V f(v). The minimum cost of a dominating broadcast is the broadcast domination number of G. In this chapter, we survey selected results on the broadcast domination number of a graph.

The research of the author Michael A. Henning supported in part by the University of Johannesburg.

The research of the author Gary MacGillivray supported by the Natural Sciences and Engineering Research Council of Canada.

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Author information

Authors and Affiliations

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

    Michael A. Henning

  2. Department of Mathematics and Statistics, University of Victoria, V8W 2Y2, P.O. Box 1700 STN CSC, Victoria, BC, Canada

    Gary MacGillivray

  3. Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, 2006, South Africa

    Feiran Yang

  4. Department of Mathematics and Statistics, University of Victoria, V8W 2Y2, P.O. Box 1700 STN CSC, Victoria, BC, Canada

    Feiran Yang

Authors
  1. Michael A. Henning
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  2. Gary MacGillivray
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  3. Feiran Yang
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Corresponding author

Correspondence to Gary MacGillivray .

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, East Tennessee State University, Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa, 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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Henning, M.A., MacGillivray, G., Yang, F. (2021). Broadcast Domination in Graphs. In: Haynes, T.W., Hedetniemi, S.T., Henning, M.A. (eds) Structures of Domination in Graphs . Developments in Mathematics, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-030-58892-2_2

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