Original scientific paper

The Edge Version of the Szeged Index

Ivan Gutman ; Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Ali Reza Ashrafi ; Faculty of Science, University of Kashan, Kashan, Iran

Abstract

The Szeged index is a molecular structure descriptor equal to the sum of products nu(e đ G) ⋅
nn(e | G) over all edges e = (uv) of the molecular graph G, where nu(e | G) is the number of vertices
whose distance to vertex u is smaller than the distance to vertex v, and where nv(e | G) is
defined analogously. We now examine the edge version of the Szeged index: the sum of products
mu(e | G)∙mv(e | G) over all edges e = (uv) of the molecular graph G, where mu(e | G) is
the number of edges whose distance to vertex u is smaller than the distance to vertex v, and
where mv(e | G) is defined analogously. The basic properties of this novel structure descriptor
are established. Most of these are analogous to the properties of the ordinary Szeged index, but
some remarkable differences are also recognized.

Keywords

Szeged index; vertex-Szeged index; edge-Szeged index; PI index; vertex-PI index; edge-PI index; chemical graph theory

Hrčak ID:

28151

URI

https://hrcak.srce.hr/28151

Publication date:

30.6.2008.

Visits: 2.273 *