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Wheel Graph Formula:
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A wheel graph is a type of graph formed by connecting a single central vertex to all vertices of a cycle. It consists of a hub connected to a rim, where the rim forms a cycle around the hub.
The calculator uses the wheel graph formula:
Where:
Explanation: The formula calculates the number of branches (edges) in a wheel graph based on the number of nodes. Each node on the rim connects to the central hub and to adjacent rim nodes.
Details: Understanding wheel graph properties is important in graph theory, network design, and computer science applications where hub-and-spoke topologies are used.
Tips: Enter the number of nodes in the wheel graph. The minimum number of nodes required is 2.
Q1: What is the minimum number of nodes in a wheel graph?
A: The minimum number of nodes is 2, which forms a simple path between the hub and one rim node.
Q2: How is a wheel graph different from a star graph?
A: A wheel graph includes connections between rim nodes forming a cycle, while a star graph only has connections from the hub to rim nodes without rim connections.
Q3: What are real-world applications of wheel graphs?
A: Wheel graphs are used in network design, transportation systems, and computer network topologies where a central node connects to multiple peripheral nodes.
Q4: How many branches does a wheel graph with 5 nodes have?
A: A wheel graph with 5 nodes has 2 × (5 - 1) = 8 branches.
Q5: Can wheel graphs be used in circuit design?
A: Yes, wheel graph topologies can be applied in circuit design for efficient routing and connectivity patterns.