Geodesic
A remark on branch weights in countable trees
Mathematica Bohemica, Tome 129 (2004) no. 1, pp. 29-31

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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.
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.
DOI : 10.21136/MB.2004.134108
Classification : 05C05
Keywords: branch weight; branch weight centroid; tree; path; degree of a vertex 
Zelinka, Bohdan. A remark on branch weights in countable trees. Mathematica Bohemica, Tome 129 (2004) no. 1, pp. 29-31. doi: 10.21136/MB.2004.134108
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