Automated Conjecture Making: Domination on Planar Graphs

Abstract

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 ∈ 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 γ(G). Automated conjecture making is the process of having a computer generate conjectures. We investigate and find a bound for the domination number of planar graphs with the use of automated conjecture making