Johnathan Gross, graph theory professor at Columbia University (and holder of graphtheory.com), has composed the following graph theory song:

My Favorite Graphs
by Jonathan Gross

Labeled, bipartite, complete and directed;
transitive, rigid, and strongly connected.
Tournaments, trees; null and empty for laughs;
These are a few of my favorite graphs ...

Colors and voltages, brightly adorning,
new special cases that greet each new morning.
Hamilton circuits thru each vertex go,
Minimum cut equals maximum flow ...

Think of Polya, Kuratowski --
Heawood, Cayley, and Euler before.
Inspiring us now to work hard to derive
graph theorems evermore.