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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Murat Ersen Berberler
Faculty of Science, Department of Computer Science, Dokuz Eylul University, 35160, Izmir/Turkey
Electrical & Electronics Engineering

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Independent strong domination in complementary prisms Zeynep Nihan Berberler; Murat Ersen Berberler
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 1 (2020): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2020.8.1.1

Abstract

Let G = (V, E) be a graph and u,v ∈ V. Then, u strongly dominates  v if (i) uv ∈ E  and (ii) deg(u) ≥ deg(v). A set D ⊂ 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 ⊆ 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 Ġ   be the complement of a graph G. The complementary prism GĠ  of G  is the graph formed from the disjoint union of G  and  Ġ by adding the edges of a perfect matching between the corresponding vertices of G and Ġ. 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.
Co-Authors Zeynep Nihan Berberler