1 Ocak 2022 Dergi makalesi Açık Erişim

Dettlaff, Magda; Gozupek, Didem; Raczek, Joanna

Citation Style Language JSON

{
  "DOI": "10.1007/s10878-022-00873-y", 
  "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) <= 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).", 
  "author": [
    {
      "family": "Dettlaff", 
      "given": " Magda"
    }, 
    {
      "family": "Gozupek", 
      "given": " Didem"
    }, 
    {
      "family": "Raczek", 
      "given": " Joanna"
    }
  ], 
  "container_title": "JOURNAL OF COMBINATORIAL OPTIMIZATION", 
  "id": "260723", 
  "issue": "2", 
  "issued": {
    "date-parts": [
      [
        2022, 
        1, 
        1
      ]
    ]
  }, 
  "page": "921-933", 
  "title": "Paired domination versus domination and packing number in graphs", 
  "type": "article-journal", 
  "volume": "44"
}