In a star network, how many lines are required for connecting N nodes to the host node?
N – 1
Understanding Star Network Connectivity
A star network is a network topology where every node (computer, printer, etc.) is connected to a central hub, switch, or computer, often called the host node or central node. In this configuration, all data passes through the central device before being routed to its destination. This topology is simple to install and manage, and failure of a single peripheral node does not affect the rest of the network.
Analyzing Connections in a Star Network
The question asks about the number of lines required to connect N nodes to the host node in a star network. Let's consider what this means:
- We have a total of N nodes in the network.
- One of these N nodes is designated as the central host node.
- The remaining nodes are the peripheral nodes that need to connect to the host.
If there are N total nodes and one is the host, the number of peripheral nodes is:
\( \text{Number of peripheral nodes} = \text{Total nodes} - \text{Host node} \)
\( \text{Number of peripheral nodes} = N - 1 \)
In a star topology, each peripheral node needs a dedicated, direct connection (a line) to the central host node. Since there are \( N - 1 \) peripheral nodes, and each requires one line to connect to the host, the total number of lines required for connecting these \( N - 1 \) peripheral nodes to the single host node is \( N - 1 \).
Let's illustrate with an example:
- Suppose \( N = 4 \) nodes.
- One node is the host.
- This leaves \( 4 - 1 = 3 \) peripheral nodes.
- Each of these 3 peripheral nodes needs one line to the host.
- Total lines required: 3. This matches \( N - 1 = 4 - 1 = 3 \).
The connections in a star network can be visualized as spokes radiating from the central hub (the host node).
Consider the different options provided:
- \( N + 1 \): This would imply more lines than nodes, which doesn't fit the star topology where each peripheral node has only one connection to the center.
- \( N/2 \): This formula does not consistently represent the number of connections based on the total number of nodes in a star network.
- \( (N/2) - 1 \): Similar to the above, this does not accurately describe the connectivity requirement of a star network.
- \( N - 1 \): This formula correctly represents the number of lines needed, as there are \( N - 1 \) peripheral nodes each requiring a connection to the central host node.
Therefore, in a star network with N total nodes (where one is the host), \( N - 1 \) lines are necessary to connect the peripheral nodes to the central host.
Number of Lines Calculation
Let \( N \) be the total number of nodes in the star network.
Number of host nodes = 1
Number of peripheral nodes = \( N - 1 \)
Each peripheral node connects directly to the host node with one line.
Total lines = (Number of peripheral nodes) \( \times \) (Lines per peripheral node to host)
Total lines = \( (N - 1) \times 1 = N - 1 \)
So, \( N - 1 \) lines are required.
Conclusion
Based on the structure and connectivity requirements of a star network topology, where all peripheral nodes connect directly to a single central host node, the number of lines required for connecting N nodes (including the host) to the host node is \( N - 1 \).
| Number of Total Nodes (N) | Number of Host Nodes | Number of Peripheral Nodes (N-1) | Lines Required (N-1) |
|---|---|---|---|
| 2 | 1 | 1 | 1 |
| 3 | 1 | 2 | 2 |
| 4 | 1 | 3 | 3 |
| 5 | 1 | 4 | 4 |
Revision Table: Star Network Connectivity
| Concept | Description | Lines Formula (N total nodes) |
|---|---|---|
| Star Network | All nodes connect to a central hub/host. | \( N - 1 \) |
| Host Node | The central node in the star topology. | - |
| Peripheral Node | A node connected directly to the host node. | - |
| Connection Lines | Direct link between a peripheral node and the host. | \( N - 1 \) (total) |
Additional Information: Network Topologies
Network topology refers to the physical or logical arrangement of connected devices in a network. Understanding different topologies is crucial in computer networking.
- Bus Topology: All devices share a single communication line (bus). If the bus breaks, the entire network fails. Requires \( N \) taps to connect \( N \) nodes.
- Ring Topology: Devices are connected in a closed loop. Data travels in one direction around the ring. Requires \( N \) lines to connect \( N \) nodes.
- Mesh Topology: Every node is connected to every other node. Provides high redundancy but is complex and expensive to set up. Requires \( \frac{N(N-1)}{2} \) lines for \( N \) nodes in a full mesh.
- Star Topology: As discussed, all nodes connect to a central point. \( N - 1 \) lines for \( N \) nodes.
- Tree Topology: A hierarchical structure, often combining characteristics of bus and star topologies.
- Hybrid Topology: A combination of two or more different topologies.
Each topology has its own advantages and disadvantages regarding cost, complexity, reliability, and performance. The star network's simplicity in wiring and fault isolation makes it very common, especially in Local Area Networks (LANs).
Important Questions from Networking
In Gmail, what do you use when you receive a mail and want to send the mail in response of the same mail and to the original sender only?
- _______ are rules that exist at several levels in a telecommunication connection.
_______ is a type of dedicated file storage device that provides local-area network (LAN) users with centralized, consolidated disk storage through a standard Ethernet connection.
_______ is also known as protocol convertor.
Which of the following Internet protocol specifies how data is exchanged over the Internet and how it should be broken into IP packets?
