Author:
Kramer Marie,Rautenbach Dieter
Abstract
AbstractFor a graph G, and two distinct vertices u and v of G, let $$n_{G}(u,v)$$
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 $$|n_{G}(u,v)-n_{G}(v,u)|$$
|
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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Chemistry
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