Minimum Total Dominating Energy of Some Special Classes of Graphs
K. Malathy1, S. Meenakshi2
1K. Malathy, Research Scholar, Department of Mathematics, VISTAS, Chennai (Tamil Nadu), India.
2Dr. S. Meenakshi, Associate Professor, Department of Mathematics, VISTAS, Chennai (Tamil Nadu), India.
Manuscript received on 19 January 2020 | Revised Manuscript received on 02 February 2020 | Manuscript Published on 05 February 2020 | PP: 221-226 | Volume-8 Issue-4S5 December 2019 | Retrieval Number: D10091284S519/2019©BEIESP | DOI: 10.35940/ijrte.D1009.1284S519
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Let 𝑮 = (𝑽,𝑬) be a simple, finite, connected and undirected graph with vertex set V(G) and edge set E(G). Let 𝑺 ⊆ 𝑽(𝑮). A set S of vertices of G is a dominating set if every vertex in 𝑽 𝑮 − 𝑺 is adjacent to at least one vertex in S. A set S of vertices in a graph 𝑮(𝑽,𝑬) is called a total dominating set if every vertex 𝒗 ∈ 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 𝜸𝒕 (𝑮). 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.
Keywords: Dominating Set, Minimum Total Dominating Set, Minimum Total Dominating Matrix, Minimum Total Dominating Eigen Values, Minimum Total Dominating Energy of A Graph.
Scope of the Article: Cryptography and Applied Mathematics