G-2009-30
On a Conjecture About the Szeged Index
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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.
Published June 2009 , 10 pages
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Jan 2010
On a conjecture about the Szeged index
and
European Journal of Combinatorics, 31(7), 1662–1666, 2010
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