How to Formally define $\delta$ in a DFA? I have made a draw of a DFA, and I have to formally define the automaton in the following format. Let $A$ be the necessary automaton :
$$A=&lt;\Sigma,Q,q_0,\delta,F&gt;$$

Where $\Sigma=\{a,b,c\}, Q=\{q_0,...,q_4\}, F=q_3$ and $q_0$ is the initial state.

The drawing is attached to this post:

Can I do something like $\delta_{A}(q_0,\sigma)=q_1$ for each state? should I unite a few states together?

Thank you!
You're over-thinking this.

You need to define the value of $\delta(q,\sigma)$ for every $q\in Q$ and $\sigma\in\Sigma$ and, ideally, make it clear that you have done so. What format you use is a matter of your and your instructor's personal preferences.