Using the AutoGraphiX 2 system, a systematic study is made on generation and proof of relations of the form

where $\overline{l}$ denotes the average distance between distinct vertices of a connected graph G, i one of the invariants: diameter, radius, girth, maximum, average and minimum degree, $\underline{b}n$ and $\overline{b}n$ are best possible lower and upper bounds, functions of the order n of G and $\oplus \in { -,+ \times, /}$. In 24 out of 48 cases simple bounds are obtained and proved by the system. In 21 more cases, the system provides bounds, 16 of which are proved by hand.