Option $(D)$ : Binary heap. $|E|$ decrease key operations and each taking $O\left(\log|V|\right)$ time $+$ $|V|$ extract-min operations each taking $O\left(\log|V|\right)$.
Option $(B)$ : Fibonacci heap. $|E|$ decrease key operations and each taking $O(1)$ time $+$ $|V|$ extract-min operations each taking $O\left(\log|V|\right)$.
Option $(A)$ : Array. Finding min-vertex in each iteration takes $O(V)$ and this needs to be done $|V|$ times.
Binomial Heap is same as Binary heap here, as the critical operations are decrease key and extract-min.
Correct Answer: $D$