MINIMUM TOTAL DOMINATING HYPERENERGETIC GRAPHS

Let G be a simple graph with vertex set V(G) and edge set E(G). A set S of vertices in a graph G(V, E) is called a total dominating set if every vertex u is an element of V is adjacent to an element of S. The minimum cardinality of a total dominating set of G is called the total domination number of G which is denoted by gamma(t)(G). The energy of the graph is defined as the sum of the absolute values of the eigenvalues of the adjacency matrix. The graphs whose energy is greater than that of complete graph are called hyperenergetic, i.e. E(G)>2n-2. In this paper, we computed minimum total dominating hyperenergetic of some standard graph such as Friendship graph, Wheel graph and Star Graph and compared the energy by plotting the graph.