Let G be an arbitrary graph with vertex set {1,2, ...,N} and degrees d i ≤ D, for fixed D and all i, then for the index R′(G) = Σi<jdjdjRij we show that R′(G) ≥ 2 |E| (N - 2 + 1/D + 1). We also show that the minimum of R′(G) over all N-vertex graphs is attained for the star graph and its value is 2N2 - 5N + 3. © 2010 Wiley Periodicals, Inc.