Relations are established between the first and second Zagreb index (M-1, and M-2) of the graph of atomic orbitals (G*), and of the ordinary hydrogen-depleted (G(C)) and hydrogen-filled (G(H)) molecular graphs of saturated hydrocarbons. It is shown that M-1(G*) = 12 M-1 (G(C)) + 9 M-1 (G(H)) + 96 (c - 1) and M-2 (G*) = 36 M-2 (G(C)) + 15 M-2(G(H)) + 54 M-1(G(C)) + 96 (c - 1), where c is the number of (independent) cycles of the underlying molecule.