All graphs with paired-domination number two less than their order

Włodzimierz Ulatowski

doi:10.7494/opmath.2013.33.4.763

All graphs with paired-domination number two less than their order

Abstract

Let G=(V,E) be a graph with no isolated vertices. A set S⊆V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number γp(G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199-206] Haynes and Slater described graphs G with γp(G)=n and also graphs with γp(G)=n−1. In this paper we show all graphs for which γp(G)=n−2.

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Włodzimierz Ulatowski dr

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DOI:: Digital Object Identifier (open in new tab) 10.7494/OpMath.2013.33.4.763
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Keywords

PAIRED-DOMINATION

Details

Category:: Articles
Type:: artykuły w czasopismach recenzowanych i innych wydawnictwach ciągłych
Published in:: Opuscula Mathematica no. 33, edition 4, pages 763 - 783,
ISSN: 1232-9274
Language:: English
Publication year:: 2013
Bibliographic description:: Ulatowski W.: All graphs with paired-domination number two less than their order// Opuscula Mathematica. -Vol. 33., iss. 4 (2013), s.763-783
DOI:: Digital Object Identifier (open in new tab) 10.7494/opmath.2013.33.4.763
Verified by:: Gdańsk University of Technology