Double domination in rooted product graphs

Identifier:  imarina:9324073

Handle: https://hdl.handle.net/20.500.11797/imarina9324073

Authors:  Cabrera-Martinez, Abel; Estrada-Moreno, Alejandro

Abstract:
A set D of vertices of a graph G is a double dominating set of G if |N[v]∩D|≥2 for every v∈V(G), where N[v] represents the closed neighbourhood of v. The double domination number of G is the minimum cardinality among all double dominating sets of G. In this article, we show that if G and H are graphs with no isolated vertex, then for any vertex v∈V(H) there are six possible expressions, in terms of domination parameters of the factor graphs, for the double domination number of the rooted product graph G∘vH. Additionally, we characterize the graphs G and H that satisfy each of these expressions.