Independent strong domination in complementary prisms

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BERBERLER Z. N., BERBERLER M. E.

ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS, cilt.8, sa.1, ss.1-8, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.5614/ejgta.2020.8.1.1
  • Dergi Adı: ELECTRONIC JOURNAL OF GRAPH THEORY AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.1-8
  • Anahtar Kelimeler: domination, independent strong domination, complementary prisms, corona product, WEAK DOMINATION, BOUNDS, NUMBER
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Let G = (V, E) be a graph and u, v is an element of V. Then, u strongly dominates v if (i) uv is an element of E and (ii) deg(u) >= deg(v). A set D subset of V is a strong-dominating set of G if every vertex in V - D is strongly dominated by at least one vertex in D. A set D subset of V is an independent set if no two vertices of D are adjacent. The independent strong domination number is(G) of a graph G is the minimum cardinality of a strong dominating set which is independent. Let i(s)(G) be the complement of a graph G. The complementary prism G (G) over bar of G is the graph formed from the disjoint union of G and (G) over bar by adding the edges of a perfect matching between the corresponding vertices of G and (G) over bar. In this paper, we consider the independent strong domination in complementary prisms, characterize the complementary prisms with small independent strong domination numbers, and investigate the relationship between independent strong domination number and the distance-based parameters.