GRAPHS WITH THE SAME PERIPHERAL AND CENTER ECCENTRIC VERTICES

The eccentricity e(v )o f av ertexv is the distance from v to a vertex farthest from v ,a ndu 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 PeriG). We use Cep(G) to denote the set of eccentric vertices of vertices in C(G). A graph G is called an S-graph if Cep(G )=P eri(G). In this paper we characterize S-graphs with diameters less or equal to four, give some constructions of S-graphs and investigate S-graphs with one central vertex. We also correct and generalize some results of F. Gliviak.