Geodesic
The first to $(k+1)$-th smallest Wiener (hyper-Wiener) indices of connected graphs
Kragujevac Journal of Mathematics, Tome 32 (2009) no. 1.

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Let $n$ and $k$ be two nonnegative integers with $n>2k$, this paper presents the first to $(k+1)$-th smallest Wiener indices, and the first to $(k+1)$-th smallest hyper-Wiener indices among all connected graphs of order $n$, respectively. 
@article{KJM_2009_32_1_a9,
     author = {Liu Mu-huo and Xuezhong Tan},
     title = {The first to $(k+1)$-th smallest {Wiener} {(hyper-Wiener)} indices of connected graphs},
     journal = {Kragujevac Journal of Mathematics},
     pages = {109 - 115},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2009},
     zbl = {1199.05091},
     url = {http://geodesic.mathdoc.fr/item/KJM_2009_32_1_a9/}
}
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Liu Mu-huo; Xuezhong Tan. The first to $(k+1)$-th smallest Wiener (hyper-Wiener) indices of connected graphs. Kragujevac Journal of Mathematics, Tome 32 (2009) no. 1. http://geodesic.mathdoc.fr/item/KJM_2009_32_1_a9/