Aspire Faculty ID #12125 · Topic: CUET 2025 · Just now
CUET 2025

Which of the following statements are TRUE, where |E| represents the number of edges. 

(A). In case of a directed graph, the sum of lengths of all the adjacency list is E 

(B). For an undirected graph, the sum of the lengths of all the adjacency list is 2|E| 

(C). For a dense graph, adjacency matrix representation is preferable 

(D). The memory requirement of the adjacency matrix of a graph is dependent on the number of edges 

Choose the correct answer from the options given below:
1. (A), (B) and (D) only 
2. (A), (B) and (C) only 
3. (A), (B), (C) and (D) 
4. (B), (C) and (D) only

Solution

- (A) ✅ True: In a directed graph, each edge appears once in exactly one adjacency list ⇒ total length = \(|E|\).
- (B) ✅ True: In an undirected graph, each edge appears twice (both endpoints) ⇒ total length = \(2|E|\).
- (C) ✅ True: For dense graphs \((|E| \approx \Theta(V^2))\), adjacency matrix is preferable (fast \(O(1)\) lookups, storage \(O(V^2)\)).
- (D) ❌ False: Adjacency matrix memory depends only on \(V^2\), not on \(|E|\).

Final Answer: Option (2) — (A), (B) and (C) only

Previous 10 Questions — CUET 2025

Nearest first

Next 10 Questions — CUET 2025

Ascending by ID
Ask Your Question or Put Your Review.

loading...