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Keywords:
branch weight; branch weight centroid; tree; path; degree of a vertex
branch weight; branch weight centroid; tree; path; degree of a vertex
Summary:
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.
References:
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[2] P. J. Slater: Accretion centers: A generalization of branch weight centroids. Discr. Appl. Math. 3 (1981), 187–192. DOI 10.1016/0166-218X(81)90015-9 | MR 0619605 | Zbl 0467.05045
[3] Z. Win, Y. Myint: The cendian of a tree. Southeast Asian Bull. Math. 25 (2002), 757–767. DOI 10.1007/s100120200016 | MR 1934672
[4] B. Zelinka: Medians and peripherians of trees. Arch. Math. Brno 4 (1968), 87–95. MR 0269541 | Zbl 0206.26105
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