Arrange the following graph on the basis of number of edges in increasing order [for n > 3]

A. K_n (Complete Graph)

B. C_n (Cycle graph)

C. W_n (Wheel graph)

D. K_{n, n} (Complete Bipartite Graphs)

E. Q_n (n-cubes graph)

Choose the correct answer from the options given below:

The correct answer is Option 1.

Key Points

• Complete Graph (K_n): Has n(n−1)/2 edges.
• Cycle Graph (C_n): Has n edges.
• Wheel Graph (W_n): Has 2(n−1) edges.
• Complete Bipartite Graph (K_n,n): Has n² edges.
• n-Cube Graph (Q_n): Has n × 2ⁿ⁻¹ edges.

Additional Information

• Let us verify using n = 5:

• Now arranging based on increasing number of edges:
• → Cycle (5) < Wheel (8) < Complete (10) < Complete Bipartite (25) < n-Cube (80)
• So, the correct answer is: B,C,A,D,E.