A new upper bound on the number of edges in a geodetic graph Original Research Article

In this paper we investigate some structural characterizations of geodetic graphs and prove that if G is a central geodetic block on p vertices with diameter d ⩾ 3, and each vertex belongs to an induced cycle C2d11, then the number q of edges equals p or q ⩽ 16 p[p − 12(5d + 1) + 8]. Therefore the upper bounds of [3] have been considerably improved.