A Characterization of Cubic Graphs with Paired-Domination Number Three-Fifths Their Order |
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| Authors: | Wayne Goddard Michael A Henning |
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| Institution: | 1.School of Computing and Department of Mathematical Sciences,Clemson University,Clemson,USA;2.Department of Mathematics,University of Johannesburg,Auckland Park,South Africa |
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| Abstract: | A paired-dominating set of a graph is a dominating set of vertices whose induced subgraph has a perfect matching, while the
paired-domination number is the minimum cardinality of a paired-dominating set in the graph. Recently, Chen et al. (Acta Math
Sci Ser A Chin Ed 27(1):166–170, 2007) proved that a cubic graph has paired-domination number at most three-fifths the number
of vertices in the graph. In this paper, we show that the Petersen graph is the only connected cubic graph with paired-domination
number three-fifths its order. |
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