### Journals Information

**
Mathematics and Statistics Vol. 9(1), pp. 1 - 7 DOI: 10.13189/ms.2021.090101 Reprint (PDF) (305Kb) **

## Corporate Domination Number of the Cartesian Product of Cycle and Path

**S. Padmashini ^{1}^{,*}, S. Pethanachi Selvam ^{2}**

^{1}Research Scholar, School of Mathematics, Madurai Kamaraj University, Madurai, Tamilnadu, India

^{2}Department of Mathematics, The Standard Fireworks Rajaratnam College for Women, Sivakasi, Tamilnadu, India

**ABSTRACT**

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 , (E_{1} a subset of E) such that there should be maximum one vertex common to any two open neighborhood of different vertices in V(G[E_{1}]) and Q, the set consists of all vertices in the vertex set V_{1}, a subset of V such that there exists no vertex common to any two open neighborhood of different vertices in V_{1}. 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 .

**KEYWORDS**

Cartesian Product, Domination, Perfect Dominating Set, Edge-Induced Sub Graph, Corporate Dominating Set, Corporate Domination Number

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] S. Padmashini , S. Pethanachi Selvam , "Corporate Domination Number of the Cartesian Product of Cycle and Path," Mathematics and Statistics, Vol. 9, No. 1, pp. 1 - 7, 2021. DOI: 10.13189/ms.2021.090101.

(b). APA Format:

S. Padmashini , S. Pethanachi Selvam (2021). Corporate Domination Number of the Cartesian Product of Cycle and Path. Mathematics and Statistics, 9(1), 1 - 7. DOI: 10.13189/ms.2021.090101.