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 (MSC 1991): 05C12, 05C35
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