complete graph
all vertices are adjacent to each other
A complete graph is a graph in which every pair of distinct vertices is connected by a unique edge. In other words, a complete graph is a graph with all possible edges present. A complete graph with n vertices is denoted by K_n, and it has n(n-1)/2 edges.
For example, K_4 is a complete graph with 4 vertices, and it has (4×3)/2=6 edges. The graph can be drawn as a square with all the edges connecting the vertices to each other. The vertex set of K_4 is {a,b,c,d}, and the edge set is {(a,b), (a,c), (a,d), (b,c), (b,d), (c,d)}.
Complete graphs are useful in various areas of mathematics, computer science, and physics. They are used, for example, in combinatorial optimization problems, in the design of algorithms, in network analysis, and in the study of social and biological networks.
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