Abstract. We study graphs of order n with the minimum value of sum-Balaban index. We show that the upper bound for the minimum value of sum-Balaban index is at most 4.47934 when n goes to infinity. 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 (2.5log(1+2.5)).25n.5+o(n.5) have the smallest value of Balaban index.