Automated Conjecturing Approach for Benzenoids

• Main Author: Muncy, David
• Format: Others
• Published: VCU Scholars Compass 2016
• Subjects: artificial intelligence; automated conjecturing; graph theory; domination; benzenoids; discrete mathematics; Artificial Intelligence and Robotics; Discrete Mathematics and Combinatorics
• Online Access: http://scholarscompass.vcu.edu/etd/4608; http://scholarscompass.vcu.edu/cgi/viewcontent.cgi?article=5685&context=etd

Benzenoids are graphs representing the carbon structure of molecules, defined by a closed path in the hexagonal lattice. These compounds are of interest to chemists studying existing and potential carbon structures. The goal of this study is to conjecture and prove relations between graph theoretic properties among benzenoids. First, we generate conjectures on upper bounds for the domination number in benzenoids using invariant-defined functions. This work is an extension of the ideas to be presented in a forthcoming paper. Next, we generate conjectures using property-defined functions. As the title indicates, the conjectures we prove are not thought of on our own, rather generated by a process of automated conjecture-making. This program, named Cᴏɴᴊᴇᴄᴛᴜʀɪɴɢ, is developed by Craig Larson and Nico Van Cleemput.