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

Author

Listed:
  • Haoli Wang

    (Dalian University of Technology)

  • Xirong Xu

    (Dalian University of Technology)

  • Yuansheng Yang

    (Dalian University of Technology)

  • Kai Lü

    (Dalian University of Technology)

Abstract

Let G=(V,E) be a graph without an isolated vertex. A set D⊆V(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 p k (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.

Suggested Citation

  • Haoli Wang & Xirong Xu & Yuansheng Yang & Kai Lü, 2011. "On the distance paired domination of generalized Petersen graphs P(n,1) and P(n,2)," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 481-496, May.
    • Handle: RePEc:spr:jcomop:v:21:y:2011:i:4:d:10.1007_s10878-009-9266-1
    DOI: 10.1007/s10878-009-9266-1
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    References listed on IDEAS

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    1. Paul Dorbec & Sylvain Gravier & Michael A. Henning, 2007. "Paired-domination in generalized claw-free graphs," Journal of Combinatorial Optimization, Springer, vol. 14(1), pages 1-7, July.
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    Cited by:

    1. Kan Yu & Mei Lu, 2014. "2-Distance paired-dominating number of graphs," Journal of Combinatorial Optimization, Springer, vol. 28(4), pages 827-836, November.

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