On Extensions of Wiener Index
نویسندگان
چکیده
Abstract The n-th order Wiener index of a molecular graph G was put forward by Estrada et al. [New J. Chem. 22 (1998) 819] as ( ) 1 ( , ) n n x W H G x where ( , ) H G x is the Hosoya polynomial. Recently Brückler et al. [Chem. Phys. Lett. 503 (2011) 336] considered a related graph invariant, ( ) 1 1 (1/ !) ( ( , )) / n n n n x W n d x H G x d x . For n=1, both W and W reduce to the ordinary Wiener index. The aim of this paper is to obtain closed formulas for these two extensions of the Wiener index. It is proved that ( ) 1 (1/ !) ( , ) n n k k W n c n k W and
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