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A characterization of graphs with disjoint dominating and paired-dominating sets

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Abstract

A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a set of vertices such that every vertex is adjacent to a vertex in the set and the subgraph induced by the set contains a perfect matching. In this paper, we provide a constructive characterization of graphs whose vertex set can be partitioned into a dominating set and a paired-dominating set.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg, 3209, South Africa

    Justin Southey & Michael A. Henning

Authors
  1. Justin Southey
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  2. Michael A. Henning
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Corresponding author

Correspondence to Michael A. Henning.

Additional information

J. Southey was supported in part by the South African National Research Foundation.

M.A. Henning was supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.

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Southey, J., Henning, M.A. A characterization of graphs with disjoint dominating and paired-dominating sets. J Comb Optim 22, 217–234 (2011). https://doi.org/10.1007/s10878-009-9274-1

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  • DOI: https://doi.org/10.1007/s10878-009-9274-1

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