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On the distance paired domination of generalized Petersen graphs P(n,1) and P(n,2)

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Abstract

Let G=(V,E) be a graph without an isolated vertex. A set DV(G) is a k -distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The minimum cardinality of a k-distance paired dominating set for graph G is the k -distance paired domination number, denoted by γ k p (G). In this paper, we determine the exact k-distance paired domination number of generalized Petersen graphs P(n,1) and P(n,2) for all k≥1.

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Correspondence to Yuansheng Yang.

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The research is supported by Chinese Natural Science Foundations (60573022), Specialized Research Fund for the Doctoral Program of Higher Education (200801411073) and Research Foundation of DLUT.

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Wang, H., Xu, X., Yang, Y. et al. On the distance paired domination of generalized Petersen graphs P(n,1) and P(n,2). J Comb Optim 21, 481–496 (2011). https://doi.org/10.1007/s10878-009-9266-1

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  • DOI: https://doi.org/10.1007/s10878-009-9266-1

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