Abstract. We study graphs of order n with the minimum value of Balaban index. We show that this value is of order Θ(n^-1). For small values of n we determine the extremal graphs and we observe that they are similar to dumbbell graphs. We show that in the class of balanced dumbbell graphs, those with clique sizes (π/2)^.25n^.5+o(n^.5) have the smallest value of Balaban index.