| Title:
|
Radius-invariant graphs (English) |
| Author:
|
Bálint, V. |
| Author:
|
Vacek, O. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
4 |
| Year:
|
2004 |
| Pages:
|
361-377 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The eccentricity $e(v)$ of a vertex $v$ is defined as the distance to a farthest vertex from $v$. The radius of a graph $G$ is defined as a $r(G)=\min _{u \in V(G)}\lbrace e(u)\rbrace $. A graph $G$ is radius-edge-invariant if $r(G-e)=r(G)$ for every $e \in E(G)$, radius-vertex-invariant if $r(G-v)= r(G)$ for every $v \in V(G)$ and radius-adding-invariant if $r(G+e)=r(G)$ for every $e \in E(\overline{G})$. Such classes of graphs are studied in this paper. (English) |
| Keyword:
|
radius of graph |
| Keyword:
|
radius-invariant graphs |
| MSC:
|
05C12 |
| MSC:
|
05C35 |
| MSC:
|
05C75 |
| idZBL:
|
Zbl 1080.05505 |
| idMR:
|
MR2102610 |
| DOI:
|
10.21136/MB.2004.134047 |
| . |
| Date available:
|
2009-09-24T22:16:21Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134047 |
| . |
| Reference:
|
[1] Buckley, F., Harary, F.: Distance in Graphs.Addison-Wesley, Redwood City, 1990. |
| Reference:
|
[2] Buckley, F., Itagi K. M., Walikar, H. B.: Radius-edge-invariant and diameter-edge-invariant graphs.Discrete Math. 272 (2003), 119–126. MR 2019205, 10.1016/S0012-365X(03)00189-4 |
| Reference:
|
[3] Buckley, F., Lewinter, M.: Graphs with all diametral paths through distant central nodes.Math. Comput. Modelling 17 (1990), 35–41. MR 1236507, 10.1016/0895-7177(93)90250-3 |
| Reference:
|
[4] Dutton, R. D., Medidi, S. R., Brigham, R. C.: Changing and unchanging of the radius of graph.Linear Algebra Appl. 217 (1995), 67–82. MR 1322543 |
| Reference:
|
[5] Frucht, R., Harary, F.: On the corona of two graphs.Aequationes Math. 4 (1970), 322–325. MR 0281659, 10.1007/BF01844162 |
| Reference:
|
[6] Gliviak, F.: On radially extremal graphs and digraphs, a survey.Math. Bohem. 125 (2000), 215–225. Zbl 0963.05072, MR 1768809 |
| Reference:
|
[7] Graham, N., Harary, F.: Changing and unchanging the diameter of a hypercube.Discrete Appl. Math. 37/38 (1992), 265–274. MR 1176857, 10.1016/0166-218X(92)90137-Y |
| Reference:
|
[8] Harary, F.: Changing and unchanging invariants for graphs.Bull. Malaysian Math. Soc. 5 (1982), 73–78. Zbl 0512.05035, MR 0700121 |
| Reference:
|
[9] Vizing, V. G.: The number of edges in a graph of given radius.Dokl. Akad. Nauk 173 (1967), 1245–1246. (Russian) Zbl 0158.42504, MR 0210622 |
| . |
