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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Le problème de trouver l’emplacement du centre et le problème de trouver la médiane dans un graphique sont importants et fondamentaux parmi de nombreux problèmes de localisation sur réseau. En relation avec ces deux problèmes, les deux théorèmes suivants sont bien connus. L'une d'elles est prouvée par Jordan et Sylvester, et montre que le centre de chaque arbre est constitué soit d'un sommet, soit de deux sommets adjacents. L'autre est prouvé par Jordan et montre que le centroïde (médiane) de chaque arbre est constitué soit d'un sommet, soit de deux sommets adjacents. Ces théorèmes ont été généralisés jusqu’à présent par de nombreux chercheurs. Harary et Norman ont prouvé que le centre de chaque graphe connecté G se trouve dans un seul bloc de G. Truszczynski a prouvé que la médiane de tout graphe connexe G se trouve dans un seul bloc de G. Slater défini k-centrum, qui peut exprimer à la fois le centre et la médiane, et a prouvé que le k-le centre de chaque arbre est constitué soit d'un sommet, soit de deux sommets adjacents. Cet article discute de la généralisation de ces théorèmes. Nous définissons le
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Masashi TAKEUCHI, Shoji SOEJIMA, "On a Relation between -Centroid and -Blocks in a Graph" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 10, pp. 2009-2014, October 2000, doi: .
Abstract: The problem of finding the location of the center and the problem of finding the median in a graph are important and basic among many network location problems. In connection with these two problems, the following two theorems are well-known. One is proved by Jordan and Sylvester, and it shows that the center of every tree consists of either one vertex or two adjacent vertices. The other is proved by Jordan and it shows that the centroid (median) of every tree consists of either one vertex or two adjacent vertices. These theorems have been generalized by many researchers so far. Harary and Norman proved that the center of every connected graph G lies in a single block of G. Truszczynski proved that the median of every connected graph G lies in a single block of G. Slater defined k-centrum, which can express both center and median, and proved that the k-centrum of every tree consists of either one vertex or two adjacent vertices. This paper discusses generalization of these theorems. We define the
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_10_2009/_p
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@ARTICLE{e83-a_10_2009,
author={Masashi TAKEUCHI, Shoji SOEJIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On a Relation between -Centroid and -Blocks in a Graph},
year={2000},
volume={E83-A},
number={10},
pages={2009-2014},
abstract={The problem of finding the location of the center and the problem of finding the median in a graph are important and basic among many network location problems. In connection with these two problems, the following two theorems are well-known. One is proved by Jordan and Sylvester, and it shows that the center of every tree consists of either one vertex or two adjacent vertices. The other is proved by Jordan and it shows that the centroid (median) of every tree consists of either one vertex or two adjacent vertices. These theorems have been generalized by many researchers so far. Harary and Norman proved that the center of every connected graph G lies in a single block of G. Truszczynski proved that the median of every connected graph G lies in a single block of G. Slater defined k-centrum, which can express both center and median, and proved that the k-centrum of every tree consists of either one vertex or two adjacent vertices. This paper discusses generalization of these theorems. We define the
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - On a Relation between -Centroid and -Blocks in a Graph
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2009
EP - 2014
AU - Masashi TAKEUCHI
AU - Shoji SOEJIMA
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2000
AB - The problem of finding the location of the center and the problem of finding the median in a graph are important and basic among many network location problems. In connection with these two problems, the following two theorems are well-known. One is proved by Jordan and Sylvester, and it shows that the center of every tree consists of either one vertex or two adjacent vertices. The other is proved by Jordan and it shows that the centroid (median) of every tree consists of either one vertex or two adjacent vertices. These theorems have been generalized by many researchers so far. Harary and Norman proved that the center of every connected graph G lies in a single block of G. Truszczynski proved that the median of every connected graph G lies in a single block of G. Slater defined k-centrum, which can express both center and median, and proved that the k-centrum of every tree consists of either one vertex or two adjacent vertices. This paper discusses generalization of these theorems. We define the
ER -