Geodesic
On the preservation of the Wiener index of cubic graphs upon vertex removal
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 285-292

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The Wiener index, $W(G)$, is the sum of distances between all vertices of a connected graph $G$. In 2018, Majstorović, Knor and Škrekovski posed the problem of finding $r$-regular graphs except cycle $C_{11}$ having at least one vertex $v$ with property $W(G)=W(G-v)$. An infinite family of cubic graphs with four such vertices is constructed.
Keywords: Wiener index
Mots-clés : distance invariant, Šoltés problem. 
A. A. Dobrynin. On the preservation of the Wiener index of cubic graphs upon vertex removal. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 285-292. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a21/
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