Closely Connected Domination Number in Corona Product of Graphs

Abstract

Let  be a simple connected graph. The vertices  are closely connected if atleast one of the shortest paths connecting them is not a cut path. A set  of vertices of a simple graph  is a CC-dominating set (closely connected dominating set) if for every vertex  there exist a vertex  such that , where  is the number of shortest paths connecting  and  except the cut paths. The minimum cordiality of a CC-dominating set is called the CC-domination number, denoted by . This paper evaluates CC- domination Number in Corona product of some standard graphs.
Objectives: Closely connected domination is new direction of Domination in Graphs, here find closely connected domination number for corona product of path, cycle with some graphs

Methods: Consider the Graph G is undirected connected simple graph. The closely connected domination number (CC- domination number) for product of graphs, which is represented as   is the minimum cardinality of Closely connected dominating set.