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Szeged index

From Wikipedia, the free encyclopedia

In chemical graph theory, the Szeged index is a topological index of a molecule, used in biochemistry. The Szeged index, introduced by Iván Gutman,[1] generalizes the concept of the Wiener index introduced by Harry Wiener. The Szeged index of a connected graph G is defined as

If e is an edge of G connecting vertices u and v, then we write e = uv or e = vu. For , let and be respectively the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u.

Szeged index plays an important role in information theory. One way to measure a network structure is through the so-called topological indices. Szeged index has been shown to correlate well with numerous biological and physicochemical properties.

Examples

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The Szeged index of Dendrimer Nanostar of the following figure can be calculated by[2]

References

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  1. ^ Gutman, I. (1994), "A formula for the Wiener number of trees and its extension to graphs containing cycles", Graph Theory Notes, NY, 27: 9–15.
  2. ^ Khalifeh, M.H.; Darafsheh, M.R; Jolany, H. (2011), "The Wiener, Szeged, and PI Indices of a Dendrimer Nanostar", Journal of Computational and Theoretical Nanoscience, 8 (2): 220–223, Bibcode:2011JCTN....8..220K, doi:10.1166/jctn.2011.1681.