The Wiener (W) and hyper-^sWiener (WW) index are two graph theoretical indices used in biochemistry. They are found to be highly correlated in [3], where the correlation between W and WW are analyzed. It is well known that W is maximized by the path and minimized by the star among trees of the same number of vertices. The problem of minimizing W for trees with a given maximum degree is studied and solved in [2] and [4]. We study and characterize the extremal trees of WW for general trees and trees with a given maximum degree.
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