Distance, Symmetry, and Topology in Carbon Nanomaterials by Ali Reza Ashrafi & Mircea V. Diudea

Author:Ali Reza Ashrafi & Mircea V. Diudea
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

where d(u, v|G) denotes the distance between the vertices u and v of G which is defined as the length of any shortest path in G connecting them. Wiener index happens to be one of the most frequently and most successfully employed structural descriptors that can be deduced from the molecular graph . Since 1976, the Wiener number has found a remarkable variety of chemical applications. Physical and chemical properties of organic substances, which can be expected to depend on the area of the molecular surface and/or on the branching of the molecular carbonatom skeleton, are usually well correlated with the Wiener index . Among them are the heats of formation, vaporization and atomization, density, boiling point, critical pressure, refractive index, surface tension and viscosity of various acyclic and cyclic, saturated and unsaturated as well as aromatic hydrocarbon species, velocity of ultrasound in alkanes and alcohols, rate of electro reduction of chlorobenzenes etc. (Gutman et al. 1993). We refer the reader to Buckley and Harary (1990); Graovac and Pisanski (1991); Gutman (1994); Diudea (1995); Dobrynin et al. (2001); John and Diudea (2004); Ashrafi and Yousefi (2007); and Putz et al. (2013), for more information about the Wiener index .

The Wiener polynomial of a graph G is defined in terms of a parameter q as follows:

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