Define complete graph.
Understand the Problem
The question is asking for the definition of a complete graph in the context of graph theory. A complete graph is a type of graph in which every pair of distinct vertices is connected by a unique edge. This means that in a complete graph with 'n' vertices, there are a total of n(n-1)/2 edges, as every vertex is connected to every other vertex.
Answer
An undirected graph where every pair of distinct vertices is connected by a unique edge.
A complete graph is an undirected graph in which every pair of distinct vertices is connected by a unique edge.
Answer for screen readers
A complete graph is an undirected graph in which every pair of distinct vertices is connected by a unique edge.
More Information
In a complete graph with n vertices, there are a total of \frac{n(n-1)}{2} edges. This property makes them significant in graph theory and combinatorial optimization.
Tips
A common mistake is not distinguishing between directed and undirected complete graphs. Ensure you specify the type correctly.
Sources
- Complete graph - Wikipedia - en.wikipedia.org
- What is Complete Graph - GeeksforGeeks - geeksforgeeks.org
- Complete Graph -- from Wolfram MathWorld - mathworld.wolfram.com
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