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The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs
Applied and Computational Mathematics
Volume 5, Issue 3, June 2016, Pages: 138-141
Received: Apr. 21, 2016; Accepted: May 3, 2016; Published: Jul. 13, 2016
Authors
Shaohui Wang, Department of Mathematics, University of Mississippi, University, MS, USA; Department of Mathematics and Computer Science, Adelphi University, Garden City, NY, USA
Mohammad Reza Farahani, Department of Applied Mathematics, Iran University of Science and Technology (IUST) Narmak, Tehran, Iran
M. R. Rajesh Kanna, Department of Mathematics, Maharani's Science College for Women, Mysore, India
Muhammad Kamran Jamil, Department of Mathematics, Riphah Institute of Computing and Applied Sciences (RICAS), Riphah International University, Lahore, Pakistan
R. Pradeep Kumar, Department of Mathematics, the National Institute of Engineering, Mysuru, India
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Abstract
Let G be a simple connected graph having vertex set V and edge set E. The vertex-set and edge-set of G denoted by V(G) and E(G), respectively. The length of the smallest path between vertices u,v V(G) is called the distance, d(u,v), between the vertices u,v. Mathematical chemistry is the area of research engaged in new application of mathematics in chemistry. In mathematics chemistry, we have many topological indices for any molecular graph, that they are invariant on the graph automorphism. In this research paper, we computing the Wiener index and the Hosoya polynomial of the Jahangir graphs J 5,m for all integer number m ≥3. The Wiener index is the sum of distances between all pairs of vertices of G as W(G)= And the Hosoya polynomial of G is H(G,x)= , where d(u,v) denotes the distance between vertices u and v.
Keywords
Regular Graphs, Connected Graphs, Jahangir Graphs, Topological Indices, Hosoya Polynomial, Wiener Index, Distances
Shaohui Wang, Mohammad Reza Farahani, M. R. Rajesh Kanna, Muhammad Kamran Jamil, R. Pradeep Kumar, The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs, Applied and Computational Mathematics. Vol. 5, No. 3, 2016, pp. 138-141. doi: 10.11648/j.acm.20160503.17
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