Szeged index of symmetric graphs /
A topological index is a numerical quantity derived in an unambigous manner from the structural graph of a molecule. These indices are graph invariants, which usually reflect molecular size and shape. The first nontrivial topological index in chemistry was introduced by H. Wiener in 1947 to study bo...
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| Format: | Book Chapter |
| Jezik: | English |
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| Sorodne knjige/članki: | Vsebovano v:
Journal of chemical information and computer sciences |
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| Izvleček: | A topological index is a numerical quantity derived in an unambigous manner from the structural graph of a molecule. These indices are graph invariants, which usually reflect molecular size and shape. The first nontrivial topological index in chemistry was introduced by H. Wiener in 1947 to study boiling points of paraffins. He originally defined his index on trees. His definition was given in terms of edge weights. Another natural generalization is called the Szeged index where the weights of edges are taken to be the product of the numbers of vertices closer to the two endpoints of the edge. Here we consider the computation of the Szeged index on symmetric graphs. We show by several examples that the symmetry can be used to obtain formulas for the Szeged index of several families of graphs. Edge contributions to the Szeged index are considered, which already proved to be useful when computing the Wiener index of symmetric graphs. The approach is analogous to the one used by Pisanski and Žerovnik in J. Chem, Inf. Comput. Sci 1994, 34, pp 395-397. It should be noted that the idea of using symmetry graphs to simplify the computation of a graph invariant is more general. An analogous approach can be used for any graph invariant that is defined in terms of edge weights. |
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| Fizični opis: | str. 77-80. |
| ISSN: | 0095-2338 |