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, Šoltés problem.
Mots-clés : distance invariant 
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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/