Strong Independent Saturation in Complementary Prisms

Abstract

The strong independent saturation number Is(G) of a graph G = (V, E) is defined as min {Is(v) : v ∈ V },where Is(v) is the maximum cardinality of a minimal strong independent dominating set of G thatcontains v. Let G¯ be the complement of a graph G . The complementary prism GG¯ of G is the graphformed from the disjoint union of G and G¯ by adding the edges of a perfect matching between thecorresponding vertices of G and G¯. In this paper, the strong independent saturation in complementaryprisms are considered, complementary prisms with small strong independent saturation numbers arecharacterized, and relationship between strong independent number and the distance-based parametersare investigated.