1 Ocak 2022 Dergi makalesi Açık Erişim

Dettlaff, Magda; Gozupek, Didem; Raczek, Joanna

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        "affiliation": "Gdansk Univ Technol, Fac Appl Phys & Math, Gdansk, Poland", 
        "name": "Dettlaff, Magda"
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      {
        "affiliation": "Gebze Tech Univ, Dept Comp Engn, Kocaeli, Turkey", 
        "name": "Gozupek, Didem"
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      {
        "affiliation": "Gdansk Univ Technol, Fac Elect Telecommun & Informat, Gdansk, Poland", 
        "name": "Raczek, Joanna"
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    "description": "Given a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by gamma(G), gamma(pr) (G), and gamma(t) (G), respectively. For a positive integer k, a k-packing in G is a set S subset of V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and is denoted by rho(k) (G). It iswell known that gamma(pr) (G) <= 2 gamma(G). In this paper, we prove that it is NP-hard to determine whether gamma(pr) (G) = 2 gamma (G) even for bipartite graphs. We provide a simple characterization of trees with.pr (G) = 2 gamma (G), implying a polynomial-time recognition algorithm. We also prove that even for a bipartite graph, it is NP-hard to determine whether gamma(pr) (G) = gamma(t) (G). We finally prove that it is both NP-hard to determine whether gamma(pr) (G) = 2 rho(4)( G) and whether gamma(pr) (G) = 2 rho(3)(G).", 
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      "issue": "2", 
      "pages": "921-933", 
      "title": "JOURNAL OF COMBINATORIAL OPTIMIZATION", 
      "volume": "44"
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    "publication_date": "2022-01-01", 
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    "title": "Paired domination versus domination and packing number in graphs"
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