Group for Research in Decision Analysis

# On a Conjecture About the Szeged Index

## Mustapha Aouchiche and Pierre Hansen

Khalifeh, Yousefi-Azari, Ashrafi and Wagner [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.

, 10 pages