Minimum Total Dominating Energy of Some Special Classes of Graphs
International Journal of Recent Technology and Engineering (IJRTE) ยท 2020
Let ๐ฎ = (๐ฝ,๐ฌ) be a simple, finite, connected and undirected graph with vertex set V(G) and edge set E(G). Let ๐บ โ ๐ฝ(๐ฎ). A set S of vertices of G is a dominating set if every vertex in ๐ฝ ๐ฎ โ ๐บ is adjacent to at least one vertex in S. A set S of vertices in a graph ๐ฎ(๐ฝ,๐ฌ) is called a total dominating set if every vertex ๐ โ ๐ฝ 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 ๐ธ๐ (๐ฎ). The energy of the graph is defined as the sum of the absolute values of the eigen values of the adjacency matrix. In this paper, we computed minimum total dominating energy of some special graphs such as Paley graph, Shrikhande graph, Clebsch graph, Chvatal graph, Moser graph and Octahedron graph.