Given a simple connected graph G = (V, E) the geodetic closure I[S] ⊂ V of a subset S of V is the union of all sets of nodes lying on some geodesic (or shortest path) joining a pair of nodes v k , v l ∈ S. The geodetic number, denoted by g(G), is the smallest cardinality of a node set S * such that I[S * ] = V. In "The geodetic number of a graph", [Harary et al. in Math. Comput. Model. 17:89-95, 1993] propose an incorrect algorithm to find the geodetic number of a graph G. We provide counterexamples and show why the proposed approach must fail. We then develop a 0-1 integer programming model to find the geodetic number. Computational results are given.
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