Using the AutoGraphiX 2 system (AGX2), we study relations between graph invariants of the form where R denotes the Randic index of a graph G = (V,E), i another invariant among matching number and the index , denotes one of the four operations , and lower and upper bounding functions of the order n of the graph considered which are tight for all n (except possibly very small values due to border effects). Conjectures are obtained in 14 out of 16 cases, 6 of which are proved automatically, 7 are proved by hand and one remains open.