### Independent strong domination in complementary prisms

#### 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 *i _{s}*(

*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.

#### Keywords

#### Full Text:

PDFDOI: http://dx.doi.org/10.5614/ejgta.2020.8.1.1

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