1 Ocak 2022 Dergi makalesi Açık Erişim

Dettlaff, Magda; Gozupek, Didem; Raczek, Joanna

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  <identifier identifierType="URL">https://aperta.ulakbim.gov.tr/record/260723</identifier>
  <creators>
    <creator>
      <creatorName>Dettlaff, Magda</creatorName>
      <givenName>Magda</givenName>
      <familyName>Dettlaff</familyName>
      <affiliation>Gdansk Univ Technol, Fac Appl Phys &amp; Math, Gdansk, Poland</affiliation>
    </creator>
    <creator>
      <creatorName>Gozupek, Didem</creatorName>
      <givenName>Didem</givenName>
      <familyName>Gozupek</familyName>
      <affiliation>Gebze Tech Univ, Dept Comp Engn, Kocaeli, Turkey</affiliation>
    </creator>
    <creator>
      <creatorName>Raczek, Joanna</creatorName>
      <givenName>Joanna</givenName>
      <familyName>Raczek</familyName>
      <affiliation>Gdansk Univ Technol, Fac Elect Telecommun &amp; Informat, Gdansk, Poland</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Paired Domination Versus Domination And Packing Number In Graphs</title>
  </titles>
  <publisher>Aperta</publisher>
  <publicationYear>2022</publicationYear>
  <dates>
    <date dateType="Issued">2022-01-01</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://aperta.ulakbim.gov.tr/record/260723</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.1007/s10878-022-00873-y</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opendefinition.org/licenses/cc-by">Creative Commons Attribution</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">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) &amp;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).</description>
  </descriptions>
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