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Connected Domination

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Topics in Domination in Graphs

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

Abstract

A set S of vertices of a connected graph G = (V, E) is a connected dominating set of G if every vertex of V − S is adjacent to at least one vertex of S and the subgraph induced by S is connected. In this chapter, we survey various results on the connected domination parameters obtained over the last 40 years.

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Acknowledgements

The authors are grateful to Dr Nacéra Meddah for her help in drawing the figures.

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Authors and Affiliations

  1. LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria

    Mustapha Chellali

  2. University Paris-Saclay (honorary), LRI-CNRS, Orsay, France

    Odile Favaron

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  1. Mustapha Chellali
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  2. Odile Favaron
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Correspondence to Mustapha Chellali .

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  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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Chellali, M., Favaron, O. (2020). Connected Domination. 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_4

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