June 6 Day 90: We Are Math Club

What does Math Club do at its last official meeting of the academic year?

• Nominate a slate of officers for the coming year.
• Plan a “drive by” celebration to: congratulate the graduating seniors; announce the results of the officer election; distribute math awards; and see friends at-a-distance-but-in-real-life for the first time in too long.
• Think about questions of directed graphs inspired by Francis Su’s Zoom Room game. People are the vertices of the digraph and the direction they point determines an arc (or possibly two if the participant boxes don’t line up exactly) of a directed graph. Assume that we are playing on a torus so that pointing off the edge wraps to the parallel side. Here is a simplified version of the directed graph from above, where the wrapped edges are redrawn more directly.

So what questions did we ask?

• Is there a directed Hamilton path? (A walk that travels along directed edges and passes through each vertex exactly once.)
• Is there a directed Hamilton cycle? (A Hamilton path that begins and ends at the same vertex.)
• Is there a directed Eulerian path? (A walk that travels each directed edge exactly once.)
• Is there a directed Eulerian circuit? (An Eulerian path that begins and ends in the same place.)
• And just because my screen doesn’t have a particular feature, does someone else’s? Because as we know, everyone has a different ordering on their own screen. Or is there some achievable Zoom ordering that does?