For n devices in a network, ________ number of duplex-mode links are required…
2014
For n devices in a network, ________ number of duplex-mode links are required for a mesh topology.
- A.
n(n + 1)
- B.
n (n – 1)
- C.
n(n + 1)/2
- D.
n(n – 1)/2
Attempted by 3549 students.
Show answer & explanation
Correct answer: D
Answer: n(n − 1)/2
Reasoning:
Each device must be connected to every other device, so each device requires (n − 1) links.
Summing links per device gives n(n − 1), but this counts each physical link twice (once from each end).
Divide by 2 to correct the double counting, giving n(n − 1)/2.
Example: For n = 4 devices, links = 4 × 3 / 2 = 6, which corresponds to the six distinct pairs of devices.
A video solution is available for this question — log in and enroll to watch it.