The number of edges of radius-invariant graphs

Abstract

ABSTRACT. The eccentricity e(v) of vertex v is defined as a distance to a farthest vertex from v. The radius of a graph G is defined as r(G) = minWe consider properties of unchanging the radius of a graph under two different situations: deleting an arbitrary edge and deleting an arbitrary vertex. This paper gives the upper bounds for the number of edges in such graphs.