On a conjecture about the Szeged index

M. Aouchiche; P. Hansen

doi:10.1016/j.ejc.2010.04.001

On a conjecture about the Szeged index

M. Aouchiche, P. Hansen

Research output: Contribution to journal › Article › peer-review

54 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 language	English
Pages (from-to)	1662-1666
Number of pages	5
Journal	European Journal of Combinatorics
Volume	31
Issue number	7
DOIs	https://doi.org/10.1016/j.ejc.2010.04.001
Publication status	Published - Oct 2010
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2010.04.001

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On a conjecture about the Szeged index

Abstract

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