Generating the nine-point graphs

Abstract

A program has been written which recently generated all the (unlabelled) nine-point graphs. Written in MACRO-10 assembly language and run on a 165K PDP-10, it generates the complete set of 274,668 graphs in less than six hours. The algorithm on which this program is based is discussed with an emphasis on coding of graphs and various programming techniques designed to save space and time during execution. The methods developed may have applications in other combinatorial generating problems.