Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
; Prairie View A&M Univ, Prairie View, TX 77429 USA
We use the permutation group of order 4 to classify the fourth order tree QCD Feynman diagrams, which contribute to the gg to t(t)over-bar-gg process. (There are 159 of them.) We also provide new methods to make the color sum, and to check the gauge symmetry of the matrix elements and Feynman parts.