The Medium Domination Number of a Jahangir Graph J m,n

In 1958 - Claude Berge introduced the domination number of a graph which is used to protect the single vertices. But in 2011 Duygu Vargor and Pinar Dundar initiated the medium domination number of a graph which is utilized to protect the pairs of vertices in a graph.

In a graph every vertices u, v ∈ V should be privileged and it is essential to scrutinize how many vertices are proficient of dominating both of u and v. We compute the total number of vertices that dominates all pairs of vertices and evaluate the average of this value and call it "the medium domination number" of graph. The medium domination number of G is the minimum cardinality among all the medium domination sets of G.

We prove the main result by two-dimensional induction method. First we are manipulative the medium domination number of J_1,3. Then we are calculating the medium domination number of J_m+1,3 and J_m,n+1. Finally we are getting the medium domination number of J_m,n. By using this method we can proficient to observe how many pairs of vertices are dominates in the Jahangir graph J_m,n.

In graph theory, there are many stability parameters such as the connectivity number, the edge-connectivity number, the independence number, the vertex domination number and the domination number. In this paper, we obtained the bound of the medium domination number of Jahangir graph J_m,n.