This is a possible duplicate of the following (but not sure it answered my question):
Is it possible to support .(any symbol) or \d, \w, \W in DFA
My professor is asking for a finite automata state diagram for some language that accepts even length strings (actually it's more complicated than that, but I'm starting with that as a subset). But he didn't define the alphabet of the language (on purpose). We can assume the alphabet is definite, but I assume I can't just use an arbitrary alphabet instance.
But what alphabet symbols / terminals should I put on the edges? It shouldn't be $\Sigma^*$. It shouldn't be $\epsilon$. Can I use $.$ ? Can I use a $*$ ? Can I use anything as long as I describe what it means?
EDIT - I just found the use of $*$ in these notes of an Illinois course (p.4):