On a relation between Szeged and Wiener indices of bipartite graphs

Document Type: Research Paper

Authors

1 Nankai University, Center for Combinatorics

2 Nankai University

3 University of Kragujevac Kragujevac, Serbia

Abstract

Hansen et‎. ‎al.‎, ‎using the AutoGraphiX software‎ ‎package‎, ‎conjectured that the Szeged index $Sz(G)$ and the‎
‎Wiener index $W(G)$ of a connected bipartite graph $G$ with $n \geq‎ ‎4$ vertices and $m \geq n$ edges‎, ‎obeys the relation‎ ‎$Sz(G)-W(G) \geq 4n-8$‎. ‎Moreover‎, ‎this bound would be the best possible‎. ‎This paper offers a proof to this conjecture‎.

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Main Subjects


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