# Graphs with the same peripheral and center eccentric vertices

Mathematica Bohemica (2000)

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

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topKyš, 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

top- Chаrtrаnd G., Lesniаk L., Graphs and Digraphs, Wadsworth and Brooks, Monterey, California, 1986. (1986)
- 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)
- 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
- Gliviаk F., Two classes of graphs related to extrernal eccentricities, Math. Bohem. 122 (1997), 231-241. (1997) MR1600875
- 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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