The Domination Number of Generalized Petersen Graphs with a Faulty Vertex

2013/05/07 by Jun-Lin Guo, Kuo-Hua Wu, Guo, Jun-Lin +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Group Theory (math.GR) #Interconnection Networks and Systems #math.CO #math.GR

paper · pdf · doi:10.48550/arxiv.1305.1366

14 pages,9 figures

openalex publication_date 2013/05/07 · arxiv created 2013/09/03 · arxiv updated 2013/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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