Is a complete graph meaningful ?

In summary, a complete graph is a type of graph where every pair of vertices is connected by an edge. It is different from other types of graphs because it has the maximum number of edges possible, making it a fully connected graph. The significance of a complete graph lies in its simplicity and efficiency in representing relationships between objects and its real-world applications. It can have any number of vertices, but the number of edges grows exponentially as the number of vertices increases. In mathematics, it is used to study graph theory, topology, and as a building block for more complex graphs, aiding in problem-solving and proof techniques.
  • #1
EddieCrash
5
0
Is "a complete graph" meaningful ?

Is "a complete graph" meaningful ?
 
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  • #2
Yes, it is. But where does the question come from?
 
  • #3
I thought no one says "a complete graph", I also don't know what it is.

Thanks for your answer, bye
 
  • #4
It has a well defined meaning in Graph Theory. But I don't know if that is what you wanted: the complete graph (with n vetices) is the one with all possible edges. They are all isomorphic, as graphs, so we can say 'the complete graph' with n vertices.
 

Related to Is a complete graph meaningful ?

1. What is a complete graph?

A complete graph is a type of graph where every pair of vertices is connected by an edge. This means that there is an edge between every possible pair of vertices in the graph.

2. How is a complete graph different from other types of graphs?

A complete graph is different from other types of graphs because it has the maximum number of edges possible. This means that every vertex is connected to every other vertex, making it a fully connected graph.

3. What is the significance of a complete graph?

A complete graph is significant because it is a simple and efficient way to represent and study relationships between objects or entities. It also has many real-world applications, such as in communication networks and transportation systems.

4. Can a complete graph have any number of vertices?

Yes, a complete graph can have any number of vertices. However, the number of edges in a complete graph is always equal to n(n-1)/2, where n is the number of vertices. This means that as the number of vertices increases, the number of edges grows exponentially.

5. How is a complete graph used in mathematics?

A complete graph is used in mathematics to study various properties and concepts, such as graph theory and topology. It is also used as a building block for more complex graphs and can help in problem-solving and proof techniques.

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