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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...

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