Is it mandatory to define transitions on every possible alphabet in Deterministic Finite Automata?
Suppose a DFA was allowed to have missing transitions.  What happens if you encounter a symbol which has no transtion defined for it?  The result is undefined.  That would seem to violate the "deterministic" characteristic of a DFA.

However, it's trivial to transform such an incomplete DFA into a complete DFA.  Simply add a new state, illegal, and map any undefined transitions to the illegal state.  Finally, add transitions for every symbol from the illegal state back to itself. This illegal state is often called a sink state, because once data falls into the sink there's no way to get out.

So, from a practical perspective, it's kind of moot, as long as you have a well-defined way to handle missing transitions.