I am reading a computer theory book and came across the following example converting a NFA to a DFA:
My question is, would you not need an edge labeled $b$ going from the $x_4$ node on the right to the null collection state?
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The standard definition of DFAs involves a transition function, that is total. That means that, from every state, there should be an arrow for each symbol. So, yes, there is a missing $b$ arrow from $q_4$ to $\emptyset$ and also, missing $a$ and $b$ arrows from $\emptyset$ to itself. While we're at it, the diagram also has no indicated start state.
Note, though, that some authors use the convention that, if there's no transition given for some symbol from some state then, when the automaton reads that symbol in that state, it goes to a "dead" state. The dead state is non-accepting and the automaton cannot leave it (reading any character keeps it in that state). The author of your book might be using that convention inconsistently: the dead state is $\emptyset$ but they've only shown some of the transitions that lead to it. I think that's bad style: in my opinion, it's clearest to either show all the transitions to the dead state, or none of them.
Indeed, if you really insist on the $\emptyset$ node, then you definitively need an edge labeled 'b' going from the x(sub 4) node to the $\emptyset$ node. In addition, the $\emptyset$ node also needs edges labeled 'a' and 'b' going back to itself.
In my opinion, the insistence on the $\emptyset$ node is misguided anyway, especially if the task is to draw the DFA.