The Connected Certified Domination Number Of Join Of Two Graphs

Abstract

A subset S from the vertex set V(G) of a graph G is known a dominating set. This means that every vertex in S must be adjacent to at least one vertex in S. Now, when we refer to a dominating set S as a certified dominating set of G, it has a special rule. Each vertex in S has either zero or at least two neighbors that are outside of S. Furthermore, a certified dominating set S can be called a connected certified dominating set if the subgraph  created by S remains connected within G. The minimum size of the connected certified dominating set is what we term the connected certified domination number, denoted as . In this study, we find the bounds for  and determine its exact value for several classes of graphs.