Graphs with the same peripheral and center eccentric vertices

Peter Kyš

On the Extension of Graphs with a Given Diameter without Superfluous Edges

Ferdinand Gliviak, Peter Kyš, Ján Plesník (1969)

Matematický časopis

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A characterization of $K_{r, s}$ -closed graphs

Pavol Híc (1989)

Mathematica Slovaca

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Two classes of graphs related to extremal eccentricities

Ferdinand Gliviak (1997)

Mathematica Bohemica

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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 $P e r i (G) \cap C e p (G) = \emptyset$ . We describe $S$ -graphs and $D$ -graphs for small radius. Then, for a given graph $H$ and natural numbers $r \geq 2$ , $n \geq 2$ , 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.

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