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Kramer, Marie; Rautenbach, Dieter
Journal of mathematical chemistry, 04/2021, Letnik: 59, Številka: 4Journal Article
For a graph G , and two distinct vertices u and v of G , let n G ( u , v ) be the number of vertices of G that are closer in G to u than to v . Miklavič and Šparl (arXiv:2011.01635v1) define the distance-unbalancedness of G as the sum of | n G ( u , v ) - n G ( v , u ) | over all unordered pairs of distinct vertices u and v of G . Confirming one of their conjectures, we show that the stars minimize the distance-unbalancedness among all trees of a fixed order.
