Edge-Coloured Graphs & Switching with S_m, A_m, & D_m

File: Edge-Coloured Graphs & Switching (PDF)

This is a relic from back when I did Math.

Around the start of my final semester as an undergraduate at the University of the Fraser Valley, when it was time to apply to graduate programs, I realized I was sorely lacking any actual research experience. I had just taken Graph Theory and wanted more of it, so I asked the instructor if she had anything I could work on. She put me in contact with her supervisor at the University of Victoria, Dr. Gary MacGillivray.

Gary not only agreed to help me, but spent no small amount of time supervising me via email and skype correspondances over the course of the following year. He also did all the work of writing this paper after I started my first semester as a graduate student at the University of Waterloo.

Our results here are focused on the groups S_m, A_m, and D_m. They are only preliminary steps towards understanding the general problem of switching edge-coloured graphs with non-abelian groups, but it was a lot of fun coming up with them and I had the pleasure of presenting them at UVic for the 3rd BC Combinatorics Day conference.