| Title:
|
Graphs with the same peripheral and center eccentric vertices (English) |
| Author:
|
Kyš, Peter |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
331-339 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
graph |
| Keyword:
|
radius |
| Keyword:
|
diameter |
| Keyword:
|
center |
| Keyword:
|
eccentricity |
| Keyword:
|
distance |
| MSC:
|
05C12 |
| MSC:
|
05C20 |
| MSC:
|
05C75 |
| idZBL:
|
Zbl 0963.05046 |
| idMR:
|
MR1790124 |
| DOI:
|
10.21136/MB.2000.126124 |
| . |
| Date available:
|
2009-09-24T21:44:02Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126124 |
| . |
| Reference:
|
[1] Chаrtrаnd G., Lesniаk L.: Graphs and Digraphs.Wadsworth and Brooks, Monterey, California, 1986. |
| Reference:
|
[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. |
| Reference:
|
[3] Buckley P., Lewinter M.: Graphs with all diametral paths through distant central vertices.Math. Comput. Modelling 17 (1993), 35-41. MR 1236507, 10.1016/0895-7177(93)90250-3 |
| Reference:
|
[4] Gliviаk F.: Two classes of graphs related to extrernal eccentricities.Math. Bohem. 122 (1997), 231-241. MR 1600875 |
| Reference:
|
[5] Ore O.: Diameters in graphs.J.Combin.Theory 5 (1968), 75-81. Zbl 0175.20804, MR 0227043, 10.1016/S0021-9800(68)80030-4 |
| . |
