Hamiltonian Subgroup Graphs
Immanuel David McLaughlin · BearWorks (Missouri State University) · 2009
Subgroup graphs have been studied by Bohannon and Reid, classifying groups which have planar subgroup graphs and groups with eulerian subgroup graphs. Many more graph theoretic properties of subgroup graphs are unknown. In this thesis we investigate the hamiltonicity of subgroup graphs, focusing primarily on rank 3 finite abelian p-group, proving that many of them have hamiltonian subgroup graphs. We also present a number of groups which do not have hamiltonian subgroup graphs, a complete classification of which cyclic groups have hamiltonian subgroup graphs, and some tools to find hamiltonian cycles in direct products of p-groups.