Graphs with the same peripheral and center eccentric vertices

Peter Kyš

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 3, page 331-339
  • ISSN: 0862-7959

Abstract

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The eccentricity e ( v ) of a vertex v is the distance from v to a vertex farthest from v , and u is an eccentric vertex for v if its distance from v is d ( u , v ) = e ( v ) . A vertex of maximum eccentricity in a graph G is called peripheral, and the set of all such vertices is the peripherian, denoted P e r i G ) . We use C e p ( G ) to denote the set of eccentric vertices of vertices in C ( G ) . A graph G is called an S-graph if C e p ( G ) = P e r i ( G ) . In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of S-graphs and investigate S-graphs with one central vertex. We also correct and generalize some results of F. Gliviak.

How to cite

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Kyš, Peter. "Graphs with the same peripheral and center eccentric vertices." Mathematica Bohemica 125.3 (2000): 331-339. <http://eudml.org/doc/248661>.

@article{Kyš2000,
abstract = {The eccentricity $e(v)$ of a vertex $v$ is the distance from $v$ to a vertex farthest from $v$, and $u$ is an eccentric vertex for $v$ if its distance from $v$ is $d(u,v) = e(v)$. A vertex of maximum eccentricity in a graph $G$ is called peripheral, and the set of all such vertices is the peripherian, denoted $\mathop PeriG)$. We use $\mathop Cep(G)$ to denote the set of eccentric vertices of vertices in $C(G)$. A graph $G$ is called an S-graph if $\mathop Cep(G) = \mathop Peri(G)$. In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of S-graphs and investigate S-graphs with one central vertex. We also correct and generalize some results of F. Gliviak.},
author = {Kyš, Peter},
journal = {Mathematica Bohemica},
keywords = {graph; radius; diameter; center; eccentricity; distance; graph; radius; diameter; center; eccentricity; distance},
language = {eng},
number = {3},
pages = {331-339},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Graphs with the same peripheral and center eccentric vertices},
url = {http://eudml.org/doc/248661},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Kyš, Peter
TI - Graphs with the same peripheral and center eccentric vertices
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 3
SP - 331
EP - 339
AB - The eccentricity $e(v)$ of a vertex $v$ is the distance from $v$ to a vertex farthest from $v$, and $u$ is an eccentric vertex for $v$ if its distance from $v$ is $d(u,v) = e(v)$. A vertex of maximum eccentricity in a graph $G$ is called peripheral, and the set of all such vertices is the peripherian, denoted $\mathop PeriG)$. We use $\mathop Cep(G)$ to denote the set of eccentric vertices of vertices in $C(G)$. A graph $G$ is called an S-graph if $\mathop Cep(G) = \mathop Peri(G)$. In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of S-graphs and investigate S-graphs with one central vertex. We also correct and generalize some results of F. Gliviak.
LA - eng
KW - graph; radius; diameter; center; eccentricity; distance; graph; radius; diameter; center; eccentricity; distance
UR - http://eudml.org/doc/248661
ER -

References

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  1. Chаrtrаnd G., Lesniаk L., Graphs and Digraphs, Wadsworth and Brooks, Monterey, California, 1986. (1986) 
  2. Buckley F., Lewïnter M., Minimal graph embeddings, eccentric vertices and the peripherian, Proc. Fifth Carribean Conference on Cornbinatorics and Computing. University of the West Indies, 1988, pp. 72-84. (1988) 
  3. Buckley P., Lewinter M., 10.1016/0895-7177(93)90250-3, Math. Comput. Modelling 17 (1993), 35-41. (1993) MR1236507DOI10.1016/0895-7177(93)90250-3
  4. Gliviаk F., Two classes of graphs related to extrernal eccentricities, Math. Bohem. 122 (1997), 231-241. (1997) MR1600875
  5. Ore O., 10.1016/S0021-9800(68)80030-4, J.Combin.Theory 5 (1968), 75-81. (1968) Zbl0175.20804MR0227043DOI10.1016/S0021-9800(68)80030-4

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