Geodesic
Wiener index of subdivisions of a tree
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1581-1586

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The Wiener index $W(T)$ of a tree $T$ is defined as the sum of distances between all vertices of $T$. The edge $k$-subdivision $T_e$ is constructed from a tree $T$ by replacing its edge $e$ with the path on $k+2$ vertices. Edge $k$-subdivisions of each of edges $e_1, e_2, \dots, e_{n-1}$ of a tree with $n$ vertices generate a family containing $n-1$ trees. A relation between quantities $W(T_{e_1}) + W(T_{e_2}) + \cdots + W(T_{e_{n-1}})$ and $W(T)$ is established.
Keywords: tree, Wiener index.
Mots-clés : graph invariant 
@article{SEMR_2019_16_a74,
     author = {A. A. Dobrynin},
     title = {Wiener index of subdivisions of a tree},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1581--1586},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a74/}
}
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A. A. Dobrynin. Wiener index of subdivisions of a tree. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1581-1586. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a74/