1 Ocak 2022 Dergi makalesi Açık Erişim

Dettlaff, Magda; Gozupek, Didem; Raczek, Joanna

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  <dc:creator>Dettlaff, Magda</dc:creator>
  <dc:creator>Gozupek, Didem</dc:creator>
  <dc:creator>Raczek, Joanna</dc:creator>
  <dc:date>2022-01-01</dc:date>
  <dc: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) &lt;= 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).</dc:description>
  <dc:identifier>https://aperta.ulakbim.gov.trrecord/260723</dc:identifier>
  <dc:identifier>oai:aperta.ulakbim.gov.tr:260723</dc:identifier>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opendefinition.org/licenses/cc-by</dc:rights>
  <dc:source>JOURNAL OF COMBINATORIAL OPTIMIZATION 44(2) 921-933</dc:source>
  <dc:title>Paired domination versus domination and packing number in graphs</dc:title>
  <dc:type>info:eu-repo/semantics/article</dc:type>
  <dc:type>publication-article</dc:type>
</oai_dc:dc>