Mathematics Seminar - 09/09/26

Abstract: A fullerene graph is a planar, 3-regular, and 3-connected graph with only pentagonal and hexagonal faces. There are fullerene graphs on n vertices for all even n ≥20 except for n = 22. These graphs arise as mathematical models of fullerene molecules in chemistry, where vertices correspond to carbon atoms and edges to covalent bonds. We propose an upper bound for the domination number of a fullerene on n vertices. This bound is developed by determining the domination number of a narrow nanotube.