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Resolving-power dominating sets

Author

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  • Stephen, Sudeep
  • Rajan, Bharati
  • Grigorious, Cyriac
  • William, Albert

Abstract

For a graph G(V,E) that models a facility or a multi-processor network, detection devices can be placed at vertices so as to identify the location of an intruder such as a thief or fire or saboteur or a faulty processor. Resolving-power dominating sets are of interest in electric networks when the latter helps in the detection of an intruder/fault at a vertex. We define a set S⊆V to be a resolving-power dominating set of G if it is resolving as well as a power-dominating set. The minimum cardinality of S is called resolving-power domination number. In this paper, we show that the problem is NP-complete for arbitrary graphs and that it remains NP-complete even when restricted to bipartite graphs. We provide lower bounds for the resolving-power domination number for trees and identify classes of trees that attain the lower bound. We also solve the problem for complete binary trees.

Suggested Citation

  • Stephen, Sudeep & Rajan, Bharati & Grigorious, Cyriac & William, Albert, 2015. "Resolving-power dominating sets," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 778-785.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:778-785
    DOI: 10.1016/j.amc.2015.01.037
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    Cited by:

    1. González, Antonio & Hernando, Carmen & Mora, Mercè, 2018. "Metric-locating-dominating sets of graphs for constructing related subsets of vertices," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 449-456.

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