# Article

Keywords:
eccentricity; central vertex; peripheral vertex
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.
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