Wiener and Hyper–Wiener Indices of Unitary Addition Cayley Graphs
C. Thilaga1, P. B. Sarasija2
1C. Thilaga, Department of Mathematics, Ponjesly College of Engineering, Nagercoil (Tamil Nadu), India.
2P. B. Sarasija, Department of Mathematics, Noorul Islam Centre for Higher Education, Kumaracoil (Tamil Nadu), India.
Manuscript received on 16 July 2019 | Revised Manuscript received on 01 August 2019 | Manuscript Published on 10 August 2019 | PP: 131-132 | Volume-8 Issue-2S3 July 2019 | Retrieval Number: B10220782S319/2019©BEIESP | DOI: 10.35940/ijrte.B1022.0782S319
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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: A topological index is a number associated to a graph. In chemical graph theory the Wiener index of a graph G, denoted by W(G) is the sum of the distance between all (unordered) pairs of vertices of G. That is, W(G) = ,where d (ui , uj) is the shortest distance between the vertices. ui and uj .The Hyper-Wiener Index WW(G) is the generalization of the Wiener index. The Hyper- Wiener Index of a graph G is, WW (G) = .The unitary addition Cayley graph Gn has a vertex set Zn = {0, 1,…, n-1} and the vertices u and v are adjacent if gcd (u+v,n) =1. In this paper Wiener index and Hyper Wiener indices of Unitary addition Cayley graph Gn is computed.
Keywords: Unitary Cayley Graphs, Unitary addition Cayleygraphs, Wiener Index and Hyper, Wiener Index. AMS Classification 2010— 05C50, 05C78.
Scope of the Article: Cryptography and Applied Mathematics