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Graphs with disjoint dominating and paired-dominating sets

  • Research Article
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Central European Journal of Mathematics

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 dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned into a dominating set and a paired-dominating set.

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Authors and Affiliations

  1. Department of Mathematics, University of Johannesburg, Auckland Park, South Africa

    Justin Southey & Michael A. Henning

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  1. Justin Southey
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  2. Michael A. Henning
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Correspondence to Justin Southey.

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Southey, J., Henning, M.A. Graphs with disjoint dominating and paired-dominating sets. centr.eur.j.math. 8, 459–467 (2010). https://doi.org/10.2478/s11533-010-0033-4

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  • DOI: https://doi.org/10.2478/s11533-010-0033-4

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