The diameter and radius of simple graphs

This paper develops some properties of simple blocks—block graphs which are determined up to isomorphism by the degrees of their vertices. It is first shown that if G is a simple block graph on six or more points, then G cannot be minimal or critical and must contain a triangle—have girth three.Then the most useful necessary conditions for a graph to be simple are established; if a graph is simple, it has diameter less than or equal to three and dradius less than or equal to two.