Corporate Domination Number of the Cartesian Product of Cycle and Path
S. Padmashini, S. Pethanachi Selvam · Mathematics and Statistics · 2021
Domination in graphs is to dominate the graph G by a set of vertices , vertex set of G) when each vertex in G is either in D or adjoining to a vertex in D. D is called a perfect dominating set if for each vertex v is not in D, which is adjacent to exactly one vertex of D. We consider the subset C which consists of both vertices and edges. Let denote the set of all vertices V and the edges E of the graph G. Then is said to be a corporate dominating set if every vertex v not in is adjacent to exactly one vertex of , where the set P consists of all vertices in the vertex set of an edge induced sub graph , (E1 a subset of E) such that there should be maximum one vertex common to any two open neighborhood of different vertices in V(G[E1]) and Q, the set consists of all vertices in the vertex set V1, a subset of V such that there exists no vertex common to any two open neighborhood of different vertices in V1. The corporate domination number of G, denoted by , is the minimum cardinality of elements in C. In this paper, we intend to determine the exact value of corporate domination number for the Cartesian product of the Cycle and Path .