Abstract
The paper is concerned with the weighted Harary indices, namely the multiplicatively weighted Harary index H-M and the additively weighted Harary index H-A. For a simple connected graph G with n vertices, m edges and k cut edges, sharp upper bounds on H-M (G) and H-A (G) are derived and the corresponding extremal graphs are characterized. From one of the established bounds, a main result of the paper [X. Li, J. B. Liu, On the reciprocal degree distance of graphs with cut vertices or cut edges, Ars Combin. 130 (2017) 303-318] follows instantly.