The geodetic hop domination number of complementary prisms

Abstract

Let [Formula: see text] be a graph and [Formula: see text] be the complement of [Formula: see text]. The complementary prism [Formula: see text] of [Formula: see text] is the graph formed from the disjoint union of [Formula: see text] and [Formula: see text] by adding the edges of a perfect matching between the corresponding vertices of [Formula: see text] and [Formula: see text]. A subset [Formula: see text] of vertices in a connected graph [Formula: see text] is called a geodetic hop dominating set of [Formula: see text] if [Formula: see text] is both a geodetic set and a hop dominating set of [Formula: see text]. The minimum cardinality of a geodetic hop dominating set of [Formula: see text] is its geodetic hop domination number and is denoted by [Formula: see text]. In this paper, we study the geodetic hop domination number of complementary prisms.