The Domination Number of Generalized Petersen Graphs with a Faulty Vertex

Jun-Lin Guo; Kuo-Hua Wu; Yue-Li Wang; Ton Kloks

The Domination Number of Generalized Petersen Graphs with a Faulty Vertex

Group Theory 2013-09-04 v2 Combinatorics

Authors: Jun-Lin Guo , Kuo-Hua Wu , Yue-Li Wang , Ton Kloks

Abstract

In this paper, we investigate the domination number of generalized Petersen graphs P(n, 2) when there is a faulty vertex. Denote by $\gamma(P(n,2))$ the domination number of P(n,2) and $\gamma(P_f(n,2))$ the domination number of P(n,2) with a faulty vertex $u_f$ . We show that $\gamma(P_f(n,2))=\gamma(P(n,2))-1$ when $n=5k+1$ or $5k+2$ and $\gamma(P_f(n,2))=\gamma(P(n,2))$ for the other cases.

Keywords

domination number generalized Petersen graphs faulty vertex graph theory combinatorics

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@article{arxiv.1305.1366,
  title  = {The Domination Number of Generalized Petersen Graphs with a Faulty Vertex},
  author = {Jun-Lin Guo and Kuo-Hua Wu and Yue-Li Wang and Ton Kloks},
  journal= {arXiv preprint arXiv:1305.1366},
  year   = {2013}
}

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14 pages,9 figures

The Domination Number of Generalized Petersen Graphs with a Faulty Vertex

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