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On the power domination number of the generalized Petersen graphs

Author

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  • Guangjun Xu

    (The University of Melbourne)

  • Liying Kang

    (Shanghai University)

Abstract

The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known domination problem in graphs. Following a set of rules for power system monitoring, a set S of vertices is defined to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S. The minimum cardinality of a power dominating set of G is the power domination number γ p (G). In this paper, we investigate the power domination number for the generalized Petersen graphs, presenting both upper bounds for such graphs and exact results for a subfamily of generalized Petersen graphs.

Suggested Citation

  • Guangjun Xu & Liying Kang, 2011. "On the power domination number of the generalized Petersen graphs," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 282-291, August.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:2:d:10.1007_s10878-010-9293-y
    DOI: 10.1007/s10878-010-9293-y
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    Cited by:

    1. Chao Wang & Lei Chen & Changhong Lu, 2016. "$$k$$ k -Power domination in block graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 865-873, February.
    2. Ou Sun & Neng Fan, 2019. "Solving the multistage PMU placement problem by integer programming and equivalent network design model," Journal of Global Optimization, Springer, vol. 74(3), pages 477-493, July.
    3. David G. L. Wang & Monica M. Y. Wang & Shiqiang Zhang, 2022. "Determining the edge metric dimension of the generalized Petersen graph P(n, 3)," Journal of Combinatorial Optimization, Springer, vol. 43(2), pages 460-496, March.
    4. Chung-Shou Liao, 2016. "Power domination with bounded time constraints," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 725-742, February.

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