Groups & Graphs 2.2, June, 1994 This new version of Groups & Graphs includes a large number of changes and improvements. Some of the changes are as follows. Graphs/Digraphs ÑÑÑÑÑÑÑÑÑÑÑÑ Digraph support is now available. A number of editing tools have been added which are specific to digraphs. Automorphism groups and strong components can be computed for digraphs. Laser printer output uses embedded PostScript to produce high resolution arrowheads. Planarity testing has been added. The planar dual is automatically constructed following the planarity test. Once a graph has been found planar, a planar layout algorithm is available. Hold the option key when clicking in a planar graph to show the corresponding structure of the dual. The flag tool has been added for plane graphs. Any face can be chosen as the outer face. The long-path algorithm has been significantly improved. The new algorithm is described in the paper "An algorithm for finding a long path in a graph", by Ben Li and William Kocay, Utilitas Mathematica, to appear. A bug that caused error=-192 in the printing of graphs has been corrected. A memory management bug that caused crashes under system 7 has been corrected. Groups ÑÑÑÑÑ Normal closure of a subgroup is now available. A bug that affected some computations of Even Subgroup has been corrected. Whenever a factor group is computed, the kernel is now also computed simultaneously. The prime factorization of the order of a group is now displayed. The input dialog box for permutations now accepts tab. The generators of a group are now named a, b, c, É Printing of groups has been improved. If you are new to Groups & Graphs, a good starting point is to select "Print Help FilesÉ" from the Help menu. This prints a hard copy of the help menus. Hardware Configurations ---------------------- Groups & Graphs is 32-bit clean. It will run on any MacIntosh of the 680x0 series. It does not use the FPU co-processor (it uses very little floating point computation). It will run on the Power PC Macs, but it requires that the "Modern Memory Manager" be turned OFF (via the Memory control panel).