Two classes of graphs related to extremal eccentricities

Ferdinand Gliviak

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 3, page 231-241
  • ISSN: 0862-7959

Abstract

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A graph G is called an S -graph if its periphery P e r i ( G ) is equal to its center eccentric vertices C e p ( G ) . Further, a graph G is called a D -graph if P e r i ( G ) ∩ C e p ( G ) = ∅ . We describe S -graphs and D -graphs for small radius. Then, for a given graph H and natural numbers r ≥ 2 , n ≥ 2 , 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.

How to cite

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Gliviak, Ferdinand. "Two classes of graphs related to extremal eccentricities." Mathematica Bohemica 122.3 (1997): 231-241. <http://eudml.org/doc/248127>.

@article{Gliviak1997,
abstract = {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 $r\ge 2$, $n\ge 2$, 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.},
author = {Gliviak, Ferdinand},
journal = {Mathematica Bohemica},
keywords = {eccentricity; central vertex; peripheral vertex; eccentricity; central vertex; peripheral vertex},
language = {eng},
number = {3},
pages = {231-241},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two classes of graphs related to extremal eccentricities},
url = {http://eudml.org/doc/248127},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Gliviak, Ferdinand
TI - Two classes of graphs related to extremal eccentricities
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 3
SP - 231
EP - 241
AB - 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 $r\ge 2$, $n\ge 2$, 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.
LA - eng
KW - eccentricity; central vertex; peripheral vertex; eccentricity; central vertex; peripheral vertex
UR - http://eudml.org/doc/248127
ER -

References

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  1. Buckley F., Harary F., Distance in Graphs, Addison-Wesley, New York, 1990. (1990) Zbl0688.05017
  2. Buckley F., Lewinter M., 10.1016/0895-7177(93)90250-3, Math. Comput. Modelling 17 (1993), no. 11, 35-41. (1993) MR1236507DOI10.1016/0895-7177(93)90250-3
  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. (1988) 
  4. Gliviak F., On radially critical graphs, Recent Advances in Graph Theory, Proc. Int. Symp. Prague 1974, Academia Press, Prague, 1975, pp. 207-221. (1974) MR0384613
  5. Lewinter M., 10.1016/S0167-5060(08)70378-9, Quo Vadis Graph Theory? (J. Gimbel, J.W. Kennedy and L. V. Quintas, eds.). Annals of Discrete Mathematics Vol. 55, Elsevier, Amsterdam, 89-92. MR1217982DOI10.1016/S0167-5060(08)70378-9

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