Terminal Wiener Index for Graph Structures

Authors: J. Baskar Babujee, J. Senbagamalar,

Abstract:

The topological distance between a pair of vertices i and j, which is denoted by d(vi, vj), is the number of edges of the shortest path joining i and j. The Wiener index W(G) is the sum of distances between all pairs of vertices of a graph G. W(G) = i

Keywords: Graph, Degree, Distance, Pendent vertex, Wiener index, Tree.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335672

References:

[1] Abbas Heydari, Ivan Gutman, Kragujevac, “On the Terminal Wiener Index of Thorn Graphs”, J. Sci., 32 (2010), 57–64.
[2] J. Baskar Babujee, J. Senbagamalar, “Wiener Index of Graphs using degree sequence”, J. of App. Math. Sci., 6(88) (2012), 4387–4395.
[3] M. Randic, J. Zupan, D. Vikic, “On representation of proteins by star-like graphs”, J. of Molecular Graphics and Modeling, 26 (2007), 290.
[4] A.A. Dobrynin, R. Entringer, I. Gutman, “Wiener Index for trees: theory and applications”, Acta Appl. Math., 66 (2001), 211.
[5] I. Gutman, Boris Futula, Miroslav Petrovic, “Terminal Wiener index”, J. Math. Chem., 46 (2009), 522–531.
[6] H. Wiener, J. Amer. Chem. Soc., 69 (1947), 17–20.
[7] Nenad Trinajstic, “Chemical Graph theory”, Vol II, CRC Press, Inc. Boca Raton, Florida, 115–116.