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MATHEMATICA BOHEMICA, Vol. 129, No. 1, pp. 29-31 (2004)
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A remark on branch weights in countable trees

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Bohdan Zelinka

* Bohdan Zelinka,* Technicka Univerzita Liberec, Pedagogicka fakulta, katedra aplikované matematiky, Voronezska 13, 460 01 Liberec, Czech Republic, e-mail: ` bohdan.zelinka@vslib.cz`

**Abstract:** Let $T$ be a tree, let $u$ be its vertex. The branch weight $b(u)$ of $u$ is the maximum number of vertices of a branch of $T$ at $u$. The set of vertices $u$ of $T$ in which $b(u)$ attains its minimum is the branch weight centroid $B(T)$ of $T$. For finite trees the present author proved that $B(T)$ coincides with the median of $T$, therefore it consists of one vertex or of two adjacent vertices. In this paper we show that for infinite countable trees the situation is quite different.

**Keywords:** branch weight, branch weight centroid, tree, path, degree of a vertex

**Classification (MSC2000):** 05C05

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