THE GEODETIC NUMBER OF A GRAPH

For two vertices u and v of an oriented graph D, the set I(u,v) consists of all vertices lying on a u v geodesic or v u geodesic in D.I fS is a set of vertices of D, then I(S) is the union of all sets I(u,v) for vertices u and v in S. The geodetic number g(D) is the minimum cardinality among the subsets S of V (D) with I(S )= V (D). In this paper, we give a partial answer for the conjecture by G. Chartrand and P. Zhang and present some results on orientable geodetic number.