Double domination in rooted product graphs

A set D of vertices of a graph G is a double dominating set of G if |N[v]nD| & GE; 2 for every v E 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 E 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 ov H. Additionally, we characterize the graphs G and H that satisfy each of these expressions. & COPY; 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).