Revised and edge revised Szeged indices of graphs

Morteza Faghani, Ali Reza Ashrafi

Abstract


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.


Keywords


Szeged index, edge Szeged index, revised Szeged index, revised edge Szeged index.

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DOI: https://doi.org/10.26493/1855-3974.269.44e

ISSN: 1855-3974

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