Topological indices, like degree distance, introduced by Dobrynin and Kochetova and Gutman were studied in mathematical chemistry. In this paper it is proved that in the class of connected graphs G of order n ≥ 4 and diameter equal to 2 such that G not ≅K_1,n-1, the minimum degree distance is reached by K_1,n-1 + e and it is conjectured that the bistar consisting of vertex disjoint stars K_1,n-3 and K_1,1 with central vertices joined by an edge has minimum degree distance in the class of connected graphs G of order n such that G not ≅ K_1,n-1.