The tree amplitudes with one gluon of negative helicity and other legs of positive helicity can be given by pure-gluon tree amplitudes where only one leg take negative helicity and other legs take positive helicity. Since the pure-gluon tree amplitudes with one leg of negative helicity and other legs of positive helicity vanish, we have The tree amplitudes with one graviton of negative helicity and other legs of positive helicity can be given by pure-gluon MHV[27] amplitudes. In this pure-gluon MHV amplitude, the two gluons corresponding to the negative helicity graviton take negative helicity. Using the relation (6b) and the expression of MHV amplitude for gluons (A11), the amplitude A (1 + g , 2 + g , 3 + g , 4 − $_{h}$) is given where we have use k$_{5}$ = k$_{4}$ . Similarly, A (1 + g , 2 + g , 3 − h , 4 + $_{h}$) = 0. Now we consider the MHV amplitudes where two legs take negative helicity and oth- ers take positive helicity. There are three independent amplitudes A (1 − g , 2 − g , 3 + g , 4 + $_{h}$), A (1 − g , 2 − g , 3 + $_{h}$, 4 + $_{h}$) and A (1 − g , 2 + g , 3 − h , 4 + $_{h}$). With the D$_{2}$ relations (6b) and (6c), the first two amplitudes can be expressed by five- and six-point pure-gluon MHV amplitudes respectively. After using some properties of the spinor helicity formalism and the fact that the two gluons corresponding to one graviton take half of the momentum of the graviton, we get the first two amplitudes 9 A (1 − g , 2 − g , 3 + g , 4 + $_{h}$) ∼ gκs$_{13}$ A (1 − g , 5 + g , 2 − g , 4 + g , 3 + g ) = gκs$_{13}$i 〈 12 〉 4 〈 15 〉〈 52 〉〈 24 〉〈 43 〉〈 31 〉 ∼ $_{gκ}$√$_{2}$ 〈 12 〉 $^{4}$[12] 〈 14 〉〈 24 〉〈 34 〉 $_{2}$. (11) A (1 + g , 2 + g , 3 + g , 4 − $_{h}$) ∼ g $^{2}$κ A (1 + g , 5 − g , 2 + g , 4 − g , 3 + g ) = gκs$_{13}$i 〈 54 〉 4 〈 15 〉〈 52 〉〈 24 〉〈 43 〉〈 31 〉 = 0 , (10) A (1 − g , 2 + g , 3 + g , 4 + $_{h}$) = A (1 − g , 2 + g , 3 + $_{h}$, 4 + $_{h}$) = 0 . (9)