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on amplitudes with one and two gravitons in addition to N gluons. Here two gluons take negative helicity and other legs take positive helicity. In Subsection IV C, we extend the dis- cussions to arbitrary tree amplitudes where N gluons are minimally coupled to M gravitons. Two gluons take negative helicity and the other N + M − 2 legs take positive helicity. We then extend the D$_{2}$ relations for amplitudes with one graviton in addition to N gluons to relations independent of the helicity configurations. We suggest D$_{2}$ relations should hold for any helicity configurations. The D$_{2}$ relation for a given amplitude is not unique. Different relations can be related by relations among partial amplitudes of gauge field. 

