Which of the following statement is false about Prim’s algorithm?

Concept: Prim's algorithm grows a Minimum Spanning Tree from a start vertex by repeatedly adding the cheapest edge that crosses from the tree to a vertex outside it (the cut property). To pick that cheapest crossing edge fast, every vertex keeps a key = the smallest edge weight connecting it to the current tree, and these keys are stored in a min-priority queue so that extract-min always returns the next vertex to attach.

Initialization: every vertex starts with key = infinity, then the start (root) vertex's key is set to 0 so it is the first one extracted. So the root's key is 0 while all other vertices begin at infinity and are lowered as cheaper edges are discovered.

Application — checking each statement against this method:

• "binomial max heap for the priority queue" — Prim's needs the MINIMUM-weight vertex each step, which a min-priority queue (min-heap) provides. A max-heap returns the largest key, so it cannot drive Prim's; this claim does not hold.

• "root key initialized to 0" — consistent with the initialization above: the start vertex's key is set to 0 (others are infinity), so this holds.

• "O(E log V) using a binary heap" — with a binary heap each of the O(E) decrease-key and O(V) extract-min operations costs O(log V), giving O(E log V); this holds.

• "O(E + V log V) using a Fibonacci heap" — a Fibonacci heap does decrease-key in O(1) amortized and extract-min in O(log V) amortized, giving O(E + V log V); this holds.

Cross-check: three statements match standard Prim's behaviour, so the single statement that is false about Prim's algorithm is the one claiming a binomial max heap can represent the priority queue.