| Title:
|
A remark on branch weights in countable trees (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
29-31 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
branch weight |
| Keyword:
|
branch weight centroid |
| Keyword:
|
tree |
| Keyword:
|
path |
| Keyword:
|
degree of a vertex |
| MSC:
|
05C05 |
| idZBL:
|
Zbl 1050.05028 |
| idMR:
|
MR2048784 |
| DOI:
|
10.21136/MB.2004.134108 |
| . |
| Date available:
|
2009-09-24T22:12:14Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134108 |
| . |
| Reference:
|
[1] O. Ore: Theory of Graphs.AMS Colloq. Publ., Providence, 1963. MR 0150753 |
| Reference:
|
[2] P. J. Slater: Accretion centers: A generalization of branch weight centroids.Discr. Appl. Math. 3 (1981), 187–192. Zbl 0467.05045, MR 0619605, 10.1016/0166-218X(81)90015-9 |
| Reference:
|
[3] Z. Win, Y. Myint: The cendian of a tree.Southeast Asian Bull. Math. 25 (2002), 757–767. MR 1934672, 10.1007/s100120200016 |
| Reference:
|
[4] B. Zelinka: Medians and peripherians of trees.Arch. Math. Brno 4 (1968), 87–95. Zbl 0206.26105, MR 0269541 |
| . |
