Automated Conjecture Making - Domination on Planar Graphs
Determining an upper bound for the radius of a plannar graph via automated conjecture making software.
Advisor: Dr. Taylor Short
A planar graph \(G=(V,E)\) is a graph that can be embedded in the plane, i.e. it can be drawn in the plane so that no edges intersect except at the vertices. A subset \(S\) of vertices in a graph \(G\) is called a dominating set if every vertex \(v\in V\) is either an element of \(S\) or is adjacent to an element of \(S\). The domination number of a graph \(G\) is the smallest cardinality of a dominating set; we denote the domination number as \(\gamma(G)\). Automated conjecture making is the process of having a computer generate conjectures. We investigate the domination number of planar graphs with the use of the automated conjecture making.