On a conjecture about the Szeged index
European Journal of Combinatorics
Use of the Szeged index and the revised Szeged index for measuring network bipartivity
Discrete Applied Mathematics
Discrete Applied Mathematics
The (revised) Szeged index and the Wiener index of a nonbipartite graph
European Journal of Combinatorics
Improved bounds on the difference between the Szeged index and the Wiener index of graphs
European Journal of Combinatorics
| Hi-index | 0.04 |
The revised Szeged index of a graph G is defined as Sz^*(G)=@?"e"="u"v"@?"E(n"u(e)+n"0(e)/2)(n"v(e)+n"0(e)/2), where n"u(e) and n"v(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, and n"0(e) is the number of vertices equidistant to u and v. Hansen et al. used the AutoGraphiX and made the following conjecture about the revised Szeged index for a connected bicyclic graph G of order n=6: Sz^*(G)@?{(n^3+n^2-n-1)/4,if n is odd ,(n^3+n^2-n)/4,if n is even . with equality if and only if G is the graph obtained from the cycle C"n"-"1 by duplicating a single vertex. This paper is to give a confirmative proof to this conjecture.