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arXiv · 1305.1366

The Domination Number of Generalized Petersen Graphs with a Faulty Vertex

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

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

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Jun-Lin Guo, Kuo-Hua Wu, Yue-Li Wang, Ton Kloks. 2013-09-03. The Domination Number of Generalized Petersen Graphs with a Faulty Vertex. https://arxiv.org/abs/1305.1366

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