Weak and strong domination in thorn graphs

Durgun D. D., Lökçü B.

Asian-European Journal of Mathematics, vol.13, no.4, 2020 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1142/s1793557120500710
  • Journal Name: Asian-European Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Dominating set, graph theory, strong domination, vulnerability, weak domination
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

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.