Olivetti Club

Chase VogeliCornell University
What isn't the Petersen graph?

Tuesday, April 20, 2021 - 4:30pm

The Petersen graph has a reputation for serving as a counterexample to overly optimistic conjectures in graph theory. One of its many notable properties is that it's the smallest example of a vertex-transitive graph which is not a Cayley graph. As it turns out, however, the Petersen graph can be realized as a certain generalization of Cayley graphs called a quasi-Cayley graph. In this talk, I'll introduce these families of graphs, give several examples, and discuss some results that tell you when an arbitrary graph belongs to one. No background is necessary aside from some familiarity with graphs and group actions, and a willingness to appreciate pictures of highly symmetric graphs.