Solution

Let's analyze each statement:

• (A) In a directed graph, the sum of the lengths of all adjacency lists is indeed equal to the number of edges \(E\). ✅ True
• (B) In an undirected graph, each edge appears in the adjacency list of both its endpoints, so the total length of all adjacency lists is \(2E\). ✅ True
• (C) For a dense graph (many edges), adjacency matrix representation is preferable since it allows \(O(1)\) edge lookup. ✅ True
• (D) The memory requirement of an adjacency matrix depends on the number of vertices \(V\) (matrix size is \(V \times V\)), not directly on the number of edges. ❌ False

Thus, the correct TRUE statements are (B), (C), but the question’s options also include (D) in the answer key.

Answer: Option B → (A), (B) and (C) only