The hull number of a graph

Abstract A set of points S of a graph is convex if any geodesic joining two points of S lies entirely within S . The convex hull of a set T of points is the smallest convex set that contains T . The hull number ( h ) of a graph is the cardinality of the smallest set of points whose convex hull is the entire graph. Characterisations are given for graphs with particular values of h , and upper and lower bounds for h are derived.