Groups of Graphs of Groups
Thomas Sibley, Mathematics
We can construct an edge colored complete graph of a group by generalizing the notion of distance in the reals. Each graph of a group has color preserving bijections called isometries, and the collection of all isometries of a group forms a new group. We have classified the isometry groups of all groups, and I will discuss in detail my part of this classification. I will discuss the use of direct products and semi-direct products for discovering isometry groups, and I will show that abelian groups and dicyclic groups are the building blocks for groups whose isometry group is twice as big as the original group.
Byrne, David, "Groups of Graphs of Groups" (2011). Honors Theses. 142.