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

Tina Novak () and Janez Žerovnik ()
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Tina Novak: University of Ljubljana, Faculty of Mechanical Engineering
Janez Žerovnik: University of Ljubljana, Faculty of Mechanical Engineering

SN Operations Research Forum, 2022, vol. 3, issue 3, 1-29

Abstract: 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.

Keywords: Linear algorithm; Cactus graph; DFS structure; Weighted k-fair domination; 05C85; 05C69 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s43069-022-00154-8

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