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Vertex-edge domination in graphs

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Abstract

In this paper we study graph parameters related to vertex-edge domination, where a vertex dominates the edges incident to it as well as the edges adjacent to these incident edges. First, we present new relationships relating the ve-domination to some other domination parameters, answering in the affirmative four open questions posed in the 2007 PhD thesis by Lewis. Then we provide an upper bound for the independent ve-domination number in terms of the ve-domination number for every nontrivial connected K 1,k -free graph, with k ≥ 3, and we show that the independent ve-domination number is bounded above by the domination number for every nontrivial tree. Finally, we establish an upper bound on the ve-domination number for connected C 5-free graphs, improving a recent bound given for trees.

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Authors and Affiliations

  1. Faculty of Economic Sciences and Management, University ofBoumerdes, Boumerdas, Algeria

    Razika Boutrig

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

    Razika Boutrig & Mustapha Chellali

  3. Department of Mathematics, East Tennessee State University, Johnson City, TN, 37614, USA

    Teresa W. Haynes

  4. Department of Mathematics, University of Johannesburg, AucklandPark, South Africa

    Teresa W. Haynes

  5. School of Computing, Clemson University, Clemson, SC, 29634, USA

    Stephen T. Hedetniemi

Authors
  1. Razika Boutrig
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  2. Mustapha Chellali
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  3. Teresa W. Haynes
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  4. Stephen T. Hedetniemi
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Corresponding author

Correspondence to Mustapha Chellali.

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Boutrig, R., Chellali, M., Haynes, T.W. et al. Vertex-edge domination in graphs. Aequat. Math. 90, 355–366 (2016). https://doi.org/10.1007/s00010-015-0354-2

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  • DOI: https://doi.org/10.1007/s00010-015-0354-2

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