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Paired Domination Vertex Critical Graphs

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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].

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China

    Xinmin Hou

  2. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada, V8W 3R4

    Michelle Edwards

Authors
  1. Xinmin Hou
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  2. Michelle Edwards
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Correspondence to Xinmin Hou.

Additional information

Xinmin Hou: Research supported by NNSF of China (No.10701068 and No.10671191).

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Hou, X., Edwards, M. Paired Domination Vertex Critical Graphs. Graphs and Combinatorics 24, 453–459 (2008). https://doi.org/10.1007/s00373-008-0806-8

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  • DOI: https://doi.org/10.1007/s00373-008-0806-8

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