The Szeged and the Wiener index of graphs

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Abstract

The Szeged index Sz is a recently introduced graph invariant, having applications in chemistry. In this paper, a formula for the Szeged index of Cartesian product graphs is obtained and some other composite graphs are considered. We also prove that for all connected graphs, Sz is greater than or equal to the sum of distances between all vertices. A conjecture concerning the maximum value of Sz is put forward.

Keywords

Distance in graphs
Wiener number
Szeged index
Graph products

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Supported by the Ministry of Science and Technology of Slovenia under the Grant J1-7036/94.

On leave from the Faculty of Science, University of Kragujevac, Kragujevac, Yugoslavia.