Question

What is the number of connections in the mesh topology having 5 devices?

• A. 10
• B. 12
• C. 20
• D. 5

Hint:

The formula for the number of connections in a fully connected mesh topology is identical to the mathematical combination formula $^{n}C_{2}$:
\[ \text{Links} = \frac{n(n-1)}{2} \]
This is a high-yield formula for networking exams!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the total number of physical duplex communication lines (connections) required to build a fully connected mesh network topology containing 5 devices.

Step 2: Formula for Mesh Topology Connections:
In a fully connected mesh topology, every single device has a dedicated point-to-point connection to every other device on the network.
For a network consisting of $n$ devices:
- Each device must connect to the other $n-1$ devices, requiring $n-1$ physical ports per device.
- The total number of physical simplex links is $n(n-1)$.
- For bidirectional duplex channels, the number of physical connections is given by the formula:
\[ \text{Number of Connections} = \frac{n(n-1)}{2} \]

Step 3: Detailed Calculation:
- We are given the number of devices, $n = 5$.
- Substituting this value into the equation:
\[ \text{Number of Connections} = \frac{5 \times (5 - 1)}{2} \]
\[ \text{Number of Connections} = \frac{5 \times 4}{2} \]
\[ \text{Number of Connections} = \frac{20}{2} = 10 \]
- Let us physically trace these connections:
- Connection 1-2, 1-3, 1-4, 1-5 (4 connections)
- Connection 2-3, 2-4, 2-5 (3 connections)
- Connection 3-4, 3-5 (2 connections)
- Connection 4-5 (1 connection)
- Total connections = $4 + 3 + 2 + 1 = 10$.

Step 4: Final Answer:
The total number of bidirectional physical connections in a mesh network of 5 devices is 10.
Hence, option (A) is the correct choice.