plotnw / minimal-prime-graphs

Code accompanying "On Generation, Structure, and Symmetries of Minimal Prime Graphs"

minimal-prime-graphs

Code accompanying Huang, Keller, Kissinger, Plotnick, Roma - On Generation, Structure, and Symmetries of Minimal Prime Graphs.

Dependencies:

• SageMath >= 9.6

Contents

• MinimalPrimeGraph.py - Contains various functions checking properties related to minimal prime graphs.
• MinimalPrimeGraphExamples.py - Contains an exhaustive list of all minimal prime graphs with a small number of vertices (n <= 11).
• Regular.py - Contains functions for constructing the regular graphs seen in section 3 of the paper.
• BaseGraphs.py- Contains a non-exhaustive list of base graphs with a small number of vertices (n <= 17).

Acknowledgments

This code was created as part of research conducted at Texas State University under NSF-REU grant DMS-1757233 and NSA grant H98230-21-1-0333 during the summer of 2021. The authors thank NSF and NSA for the financial support. The first, third, fourth, and fifth authors thank Texas State University for running the REU online during this difficult period of social distancing and providing a welcoming and supportive work environment. Those authors also thank their mentor, the second author Dr. Thomas Michael Keller, for his invaluable advice and guidance throughout this project. Professor Yong Yang, the director of the REU program, is recognized for conducting an inspiring and successful research program.