Gordian is a program to count the links and knots in a spatial graph. Linked cycles are detected using the linking number; knotted cycles are detected using the second coefficient of the Conway polynomial. The program is written in Java. The program was written by Loren Abrams, Lowell Trott and myself, and used for the following paper:
Counting Links and Knots in Complete Graphs, by Loren Abrams, Blake Mellor and Lowell Trott
Abstract: We investigate the minimal number of links and knots in complete partite graphs. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links for $K_{4,4,1}$ is 74. We also provide exact values or bounds on the minimal number of knots for all complete partite graphs with 8 vertices.
Below are links to an executable version of the Gordian program, a .zip file containing all the code, and a short User's Manual that explains how to use the program, and outlines the algorithms used.
Executable .jar file
Archive of Gordian source code
Gordian User's Manual (PDF)
Comments and questions may be sent to blake.mellor@lmu.edu. You are welcome to use and modify the code as you wish - but if you add any cool features, please share them with me!
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