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• W2185028597 abstract "The discovery of C60 bucky-ball, which has a nanometer-scale hollow spherical structure in 1985 by Kroto and Smalley revealed a new form of existence of carbon element other than graphite, diamond and amorphous carbon [1, 2]. Fullerenes are molecules in the form of cage-like polyhedra, consisting solely of carbon atoms. Suppose p, h, n and m are the number of pentagons, hexagons, carbon atoms and bonds between them, in a given fullerene F. Since each atom lies in exactly 3 faces and each edge lies in 2 faces, the number of atoms is n = (5p + 6h)/3, the number of edges is m = 3/2n = (5p + 6h)/2 and the number of faces is f = p + h. By the Euler’s formula n − m + f = 2, one can deduce that (5p + 6h)/3 – (5p + 6h)/2 + p + h = 2, and therefore p = 12, v = 2h + 20 and e = 3h + 30. This implies that such molecules made up entirely of n carbon atoms and having 12 pentagonal and (n/2 − 10) hexagonal faces, where n ≠ 22 is a natural number equal or greater than 20 [3, 4]. A molecular graph is a simple graph such that its vertices correspond to the atoms and the edges to the bonds. Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics [5-7]. Chemical graph theory is a branch of mathematical chemistry which applies graph theory to mathematical modeling of chemical phenomena [8]. This theory had an important effect on the development of the chemical sciences. Nowadays hundreds of researchers work in this area producing thousands articles annually. A graph is a collection of points and lines connecting a subset of them. The points and lines of a graph also called vertices and edges of the graph, respectively. If e is an edge of G, connecting the vertices and v, then we write e = uv and say u and v are adjacent. A connected graph is a graph such that there is a path between all pairs of vertices. Let ∑ be the class of finite graphs. A topological index is a function Top from ∑ into real numbers with this property that Top(G) = Top(H), if G and H are isomorphic. Obviously, the number of vertices and the number of edges are topological index. The Wiener index is the first reported distance based topological index and is defined as half sum of the distances between all the pairs of vertices in a molecular graph. If , ( ) x y V G ∈ then the distance ( , ) G d x y between x and y is defined as the length of any" @default.
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• W2185028597 date "2010-01-01" @default.
• W2185028597 modified "2023-09-27" @default.
• W2185028597 title "On Wiener index of special case of link of fullerenes" @default.
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