On a conjecture about the Szeged index

M. Aouchiche, P. Hansen

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)

Abstract

Khalifeh, Yousefi-Azari, Ashrafi and Wagner [M.K. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, S.G. Wagner, Some new results on distance-based graph invariants, European J. Combin. 30 (2009) 1149-1163] conjectured that for a connected graph G on n vertices and m edges with Szeged index Sz, Sz=mn2/4 if and only if G is a regular bipartite graph. In this note, we disprove this conjecture and then prove a stronger result from which it follows that the equality holds if and only if G is a transmission-regular bipartite graph.

Original languageEnglish
Pages (from-to)1662-1666
Number of pages5
JournalEuropean Journal of Combinatorics
Volume31
Issue number7
DOIs
Publication statusPublished - Oct 2010
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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