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Graphs with the same peripheral and center eccentric vertices

Peter Kyš — 2000

Mathematica Bohemica

The eccentricity $e (v)$ of a vertex $v$ is the distance from $v$ to a vertex farthest from $v$ , and $u$ is an eccentric vertex for $v$ if its distance from $v$ is $d (u, v) = e (v)$ . A vertex of maximum eccentricity in a graph $G$ is called peripheral, and the set of all such vertices is the peripherian, denoted $P e r i G)$ . We use $C e p (G)$ to denote the set of eccentric vertices of vertices in $C (G)$ . A graph $G$ is called an S-graph if $C e p (G) = P e r i (G)$ . In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of S-graphs and...

Note on the relation between radius and diameter of a graph

Ferdinand Gliviak; Peter Kyš — 1995

Mathematica Bohemica

The known relation between the standard radius and diameter holds for graphs, but not for digraphs. We show that no upper estimation is possible for digraphs. We also give some remarks on distances, which are either metric or non-metric.

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

Ferdinand Gliviak; Peter Kyš; Ján Plesník — 1969

Matematický časopis

On Irreducible Graphs of Diameter Two without Triangles

Ferdinand Gliviak; Peter Kyš; Ján Plesník — 1969

Matematický časopis

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Currently displaying 1 – 4 of 4

Graphs with the same peripheral and center eccentric vertices

Note on the relation between radius and diameter of a graph

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

On Irreducible Graphs of Diameter Two without Triangles