Weak and strong domination in thorn graphs

Durgun D. D., Lökçü B.

Asian-European Journal of Mathematics, cilt.13, sa.4, 2020 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1142/s1793557120500710
  • Dergi Adı: Asian-European Journal of Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Anahtar Kelimeler: Dominating set, graph theory, strong domination, vulnerability, weak domination
  • Manisa Celal Bayar Üniversitesi Adresli: Evet

Özet

Let G = (V,E) be a graph and u,v V. A dominating set D is a set of vertices such that each vertex of G is either in D or has at least one neighbor in D. The minimum cardinality of such a set is called the domination number of G, γ(G). u strongly dominates v and v weakly dominates u if (i) uv E and (ii) deg u ≥deg v. A set D V is a strong-dominating set, shortly sd-set, (weak-dominating set, shortly wd-set) of G if every vertex in V-D is strongly (weakly) dominated by at least one vertex in D. The strong (weak) domination number γs(γw) of G is the minimum cardinality of an sd-set (wd-set). In this paper, we present weak and strong domination numbers of thorn graphs.