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michael1x5
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Just wondering why its always denoted by the letter k.
The letter K is used to represent complete graphs because it is the first letter in the German word "komplett", which means complete.
Complete graphs are special because they have the maximum number of edges possible for a graph with a given number of vertices. This means that every vertex is connected to every other vertex.
A complete graph with n vertices has n(n-1)/2 edges. This can be derived from the fact that each vertex is connected to every other vertex, and there are n(n-1) possible connections. However, each edge is counted twice, so we divide by 2 to get the total number of edges.
Complete graphs are used as a starting point for many graph theory problems, as they are relatively simple and have a lot of connections between vertices. They also serve as a baseline for comparing the properties of other graphs.
Yes, a complete graph with at least 3 vertices will always have a Hamiltonian cycle, as every vertex is connected to every other vertex. This means that there is a path that visits every vertex exactly once and ends at the starting vertex.