**
MATHEMATICA BOHEMICA, Vol. 122, No. 3, pp. 231-241 (1997)
**

#
Two classes of graphs related to extremal eccentricities

##
Ferdinand Gliviak

* Ferdinand Gliviak*, Faculty of Mathematics and Physics, KNOM, Comenius University, 842 15 Bratislava, Mlynska dolina, Slovakia, e-mail: ` gliviak@fmph.uniba.sk`

**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 $r\ge2$, $n\ge2$, 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.

**Keywords:** eccentricity, central vertex, peripheral vertex

**Classification (MSC2000):** 05C12, 05C35

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number] [Journals Homepage]

*
© 1999--2000 ELibM for
the EMIS Electronic Edition
*