| Title:
|
Two classes of graphs related to extremal eccentricities (English) |
| Author:
|
Gliviak, Ferdinand |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
122 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
231-241 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A graph $G$ is called an $S$-graph if its periphery $\mathop Peri(G)$ is equal to its center eccentric vertices $\mathop Cep(G)$. Further, a graph $G$ is called a $D$-graph if $\mathop Peri(G)\cap\mathop Cep(G)=\emptyset$.
We describe $S$-graphs and $D$-graphs for small radius. Then, for a given graph $H$ and natural numbers $r\ge2$, $n\ge2$, we construct an $S$-graph of radius $r$ having $n$ central vertices and containing $H$ as an induced subgraph. We prove an analogous existence theorem for $D$-graphs, too. At the end, we give some properties of $S$-graphs and $D$-graphs. (English) |
| Keyword:
|
eccentricity |
| Keyword:
|
central vertex |
| Keyword:
|
peripheral vertex |
| MSC:
|
05C12 |
| MSC:
|
05C35 |
| idZBL:
|
Zbl 0898.05021 |
| idMR:
|
MR1600875 |
| DOI:
|
10.21136/MB.1997.126153 |
| . |
| Date available:
|
2009-09-24T21:25:40Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126153 |
| . |
| Reference:
|
[1] Buckley F., Harary F.: Distance in Graphs.Addison-Wesley, New York, 1990. Zbl 0688.05017 |
| Reference:
|
[2] Buckley F., Lewinter M.: Graphs with diametral paths through distant central nodes.Math. Comput. Modelling 17 (1993), no. 11, 35-41. MR 1236507, 10.1016/0895-7177(93)90250-3 |
| Reference:
|
[3] Buckley F., Lewinter M.: Minimal graph embeddings, eccentric vertices and the peripherian.Proc. Fifth Caribbean Conference on Combinatorics and Computing. University of the West Indies, 1988, pp. 72-84. |
| Reference:
|
[4] Gliviak F.: On radially critical graphs.Recent Advances in Graph Theory, Proc. Int. Symp. Prague 1974, Academia Press, Prague, 1975, pp. 207-221. MR 0384613 |
| Reference:
|
[5] Lewinter M.: Graphs with special distance properties.Quo Vadis Graph Theory? (J. Gimbel, J.W. Kennedy and L. V. Quintas, eds.). Annals of Discrete Mathematics Vol. 55, Elsevier, Amsterdam, 89-92. MR 1217982, 10.1016/S0167-5060(08)70378-9 |
| . |
