Geodesic
Revised and edge revised Szeged indices of graphs
Ars Mathematica Contemporanea, Tome 7 (2014) no. 1, pp. 153-160.

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The revised Szeged index is a molecular structure descriptor equal to the sum of products [nu(e) + n0(e) / 2] × [nv(e) + n0(e) / 2] over all edges e = uv of the molecular graph G, where n0(e) is the number of vertices equidistant from u and v, nu(e) is the number of vertices whose distance to vertex u is smaller than the distance to vertex v and nv(e) is defined analogously. In this paper, new formula for computing this molecular descriptor is presented by which it is possible to reprove most of results given in [M. Aouchiche and P. Hansen, On a conjecture about the Szeged index, European J. Combin. 31 (2010), 1662–1666]. We also present an edge version of this graph invariant. At the end of the paper an open question is presented.
DOI : 10.26493/1855-3974.269.44e
Keywords: Szeged index, edge Szeged index, revised Szeged index, revised edge Szeged index. 
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Morteza Faghani; Ali Reza Ashrafi. Revised and edge revised Szeged indices of graphs. Ars Mathematica Contemporanea, Tome 7 (2014) no. 1, pp. 153-160. doi : 10.26493/1855-3974.269.44e. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.269.44e/

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