Open AccessMinimum Total Dominating Energy of Some Special Classes of Graphs
Author(s) -
K. Malathy,
S. Meenakshi
Publication year - 2020
Publication title -
international journal of recent technology and engineering
Language(s) - English
Resource type - Journals
ISSN - 2277-3878
DOI - 10.35940/ijrte.d1009.1284s519
Subject(s) - combinatorics , mathematics , dominating set , regular graph , vertex (graph theory) , neighbourhood (mathematics) , complement graph , graph power , adjacency matrix , discrete mathematics , distance regular graph , graph energy , domination analysis , circulant graph , graph , line graph , mathematical analysis
Let = (,) be a simple, finite, connected and undirected graph with vertex set V(G) and edge set E(G). Let ⊆ (). A set S of vertices of G is a dominating set if every vertex in − is adjacent to at least one vertex in S. A set S of vertices in a graph (,) is called a total dominating set if every vertex ∈ 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 (). 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.