To calculate A (1 − g , 2 + g , 3 − h , 4 + $_{h}$), we need six-point non-MHV tree amplitudes for gluons A (1 − g , 6 + g , 3 − g , 5 + g , 4 − g , 2 + g ) and A (1 − g , 3 − g , 5 + g , 4 − g , 2 + g , 6 + g ). Using the tree amplitude with six gluons given in[25] and substituting k$_{3}$ , k$_{4}$ and k$_{5}$ , k$_{6}$ by k$_{3}$ 2 and k$_{4}$ 2 correspondingly, we get Then we substitute the amplitudes(13) into the relation(6c). The amplitude A (1 − g , 2 + g , 3 − h , 4 + $_{h}$) is given So far, we have given all the independent three- and four-point amplitudes, other three- and four-point amplitudes can be derived from these amplitudes by using a parity transfor- mation or performing an appropriate replacement on the external legs. These results are same with those given by KLT relations[17]. Then the three- and four-point tree ampli- tudes for gluons minimally coupled to graviton satisfy D$_{2}$ relations. We then expect the D$_{2}$ relations hold in all amplitudes where gluons are minimally coupled to gravitons. 10 A (1 − g , 2 − g , 3 + h , 4 + $_{h}$) ∼ κ $^{2}$[ s 2 12 A (1 − g , 6 + g , 3 + g , 5 + g , 4 + g , 2 − g ) − s$_{12}$s$_{13}$ A (1 − g , 3 + g , 5 + g , 4 + g , 2 − g , 6 + g )] = κ 2 [ s 2 $_{12}$i 〈 12 〉 4 〈 16 〉〈 63 〉〈 35 〉〈 54 〉〈 42 〉〈 21 〉 − s$_{12}$s$_{13}$ 〈 12 〉 4 〈 13 〉〈 35 〉〈 54 〉〈 42 〉〈 26 〉〈 61 $_{〉}$] = 0 . (12) A (1 − g , 6 + g , 3 − g , 5 + g , 4 − g , 2 + g ) = − 16 i [24] $^{4}$〈 13 〉 $^{2}$〈 23 〉 2 s 3 $_{12}$s 2 23 , A (1 − g , 3 − g , 5 + g , 4 − g , 2 + g , 6 + g ) = 16 i [24] $^{4}$〈 13 〉 $^{2}$〈 23 〉 2 s$_{12}$s 2 $_{13}$s 2 23 . (13) A (1 − g , 2 + g , 3 − h , 4 + $_{h}$) ∼ κ $^{2}$[ s 2 12 A (1 − g , 6 + g , 3 − g , 5 + g , 4 − g , 2 + g ) − s$_{12}$s$_{13}$ A (1 − g , 3 − g , 5 + g , 4 − g , 2 + g , 6 + g )] = − 16 i [24] $^{4}$〈 13 〉 $^{2}$〈 23 〉 2 s$_{12}$s 2 23 − 16 i [24] $^{4}$〈 13 〉 $^{2}$〈 23 〉 2 s$_{12}$s$_{13}$s 2 23 ∼ [24] $^{4}$〈 23 〉 $^{2}$〈 13 〉 2 s$_{12}$s$_{23}$s$_{13}$ . (14)