1. Paired Domination Vertex Critical Graphs.
- Author
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Hou, Xinmin and Edwards, Michelle
- Subjects
- *
GRAPHIC methods , *MATHEMATICS , *GRAPH theory , *DOMINATING set , *ALGORITHMS - Abstract
Let γ pr ( G) denote the paired domination number of graph G. A graph G with no isolated vertex is paired domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, γ pr ( G – v) < γ pr ( G). We call these graphs γ pr -critical. In this paper, we present a method of constructing γ pr -critical graphs from smaller ones. Moreover, we show that the diameter of a γ pr -critical graph is at most $$\frac{3}{2}(\gamma_{pr} (G)-2)$$ and the upper bound is sharp, which answers a question proposed by Henning and Mynhardt [The diameter of paired-domination vertex critical graphs, Czechoslovak Math. J., to appear]. [ABSTRACT FROM AUTHOR]
- Published
- 2008
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