Реферат: The Wiener index, W (G), is the sum of distances between all vertices of a connected graph G. In 2018, Majstorovic, Knor and Skrekovski posed the problem of finding r-regular graphs except the cycle of order 11 having at least one vertex with property W(G) = W (G–v). An infinite family of cubic graphs with four such vertices is presented.

Библиографическая ссылка: Dobrynin A.A.
On the preservation of the Wiener index upon removing a vertex in a cubic graph
22nd International conference "Mathematical Optimization Theory and Operations Research" 02-08 Jul 2023