Maximum graphs with a unique minimum dominating set

We present a conjecture on the maximum number of edges of a graph that has a unique minimum dominating set. We verify our conjecture for some special cases and prove a weakened version of this conjecture in general.

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Bibliographic Details
Published inDiscrete mathematics Vol. 260; no. 1; pp. 197 - 203
Main Authors Fischermann, Miranca, Rautenbach, Dieter, Volkmann, Lutz
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 06.01.2003
Elsevier
Subjects
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Domination
Exact sciences and technology
Extremal graphs
Graph theory
Information retrieval. Graph
Mathematics
Sciences and techniques of general use
Size
Theoretical computing
Unique minimum dominating set
Domination
Extremal graphs
Unique minimum dominating set
Size
Edge(graph)
Extremal graph
Domination number
Discrete mathematics
Graph theory
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Summary:We present a conjecture on the maximum number of edges of a graph that has a unique minimum dominating set. We verify our conjecture for some special cases and prove a weakened version of this conjecture in general.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(02)00670-2