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A Linear Time Algorithm for Weighted k-Fair Domination Problem in Cactus Graphs

Author

Listed:
  • Tina Novak

    (University of Ljubljana, Faculty of Mechanical Engineering
    Pipistrel Vertical Solutions d.o.o.)

  • Janez Žerovnik

    (University of Ljubljana, Faculty of Mechanical Engineering
    Institute of Mathematics, Physics and Mechanics)

Abstract

A set D of vertices in a graph G is a k-fair dominating set if every vertex not in D is adjacent to exactly k vertices in D. The weighted k-fair domination number $$\mathrm {wfd}_k(G)$$ wfd k ( G ) of a vertex-weighted graph G is the minimum weight w(D) among all k-fair dominating sets D. In addition to the weighted k-fair domination number, some auxiliary parameters are defined. It is shown that for a cactus graph, the weighted k-fair domination number and auxiliary parameters can be calculated in linear time.

Suggested Citation

  • Tina Novak & Janez Žerovnik, 2022. "A Linear Time Algorithm for Weighted k-Fair Domination Problem in Cactus Graphs," SN Operations Research Forum, Springer, vol. 3(3), pages 1-29, September.
    • Handle: RePEc:spr:snopef:v:3:y:2022:i:3:d:10.1007_s43069-022-00154-8
    DOI: 10.1007/s43069-022-00154-8
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    References listed on IDEAS

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    1. Majid Hajian & Michael A. Henning & Nader Jafari Rad, 2019. "A new lower bound on the domination number of a graph," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 721-738, October.
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