Original scientific paper

https://doi.org/10.3336/gm.47.1.02

Relationship between edge Szeged and edge Wiener indices of graphs

Mohammad Javad Nadjafi-Arani orcid.org/0000-0003-1754-6694 ; Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran
Hasan Khodashenas ; Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran
Ali Reza Ashrafi orcid.org/0000-0002-2858-0663 ; Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran

Abstract

Let G be a connected graph and ξ(G) = Sze(G) - We(G), where We(G) denotes the edge Wiener index and Sze(G) denotes the edge Szeged index of G. In an earlier paper, it is proved that if T is a tree then Sze(T) = We(T). In this paper, we continue our work to prove that for every connected graph G, Sze(G) ≥ We(G) with equality if and only if G is a tree. We also classify all graphs with ξ(G) ≤ 5. Finally, for each non-negative integer n ≠ 1 there exists a graph G such that ξ(G) = n.

Keywords

Edge Szeged index; edge Wiener index

Hrčak ID:

82568

URI

https://hrcak.srce.hr/82568

Publication date:

3.6.2012.

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