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7587523 
Journal Article 
Estimating the modified Hosoya index 
Zhou, B; Gutman, I 
2004 
1 
Match (Mülheim an der Ruhr, Germany)
ISSN: 0340-6253 
52 
183-192 
WOS:000225479100015 
A modified version of Hosoya index of a graph G is defined as Zdagger(G) = Pi(j=1)(n) root1 + lambda(j)(2), where lambda(j), j = 1,2,...,n, are the eigenvalues of G. If G is bipartite, then Zdagger coincides with two previously considered modification of the Hosoya index. If G is acyclic, then Zdagger(G) coincides also with the ordinary Hosoya index. We find an upper bound for Zdagger(G) in terms of the number of vertices, number of edges and the first Zagreb index, and characterize those graphs for which the upper bound is attained. Similar results for bipartite graphs are also obtained.