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In graph theory, a discipline within mathematics, the frequency partition of a graph is a partition of its vertices grouped by their degree. For example, the degree sequence of the left-hand graph below is and its frequency partition is 6 = 3 + 2 + 1. This indicates that it has 3 vertices with some degree, 2 vertices with some other degree, and 1 vertex with a third degree. The degree sequence of the bipartite graph in the middle below is and its frequency partition is 9 = 5 + 3 + 1. The degree sequence of the right-hand graph below is and its frequency partition is 7 = 6 + 1.
A graph with frequency partition 6 = 3 + 2 + 1.
A bipartite graph with frequency partition 9 = 5 + 3 + 1.
A graph with frequency partition 7 = 6 + 1.