The formulation and proof of several theorems in graph theory as well as in other areas of mathematics have been found after testing some special cases on a computer. Some results of this type are described in this paper. Special attention is paid to the interactive programming system ``Graph" (described in [7], the first part of this paper) in which a lot of graph theoretical algorithms have been implemented and whose purpose is, among other things, to enable quick formulation, checking, or disproving of conjectures in graph theory.