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Complete bipartite graph

In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first set is connected to every vertex of the second set.

Definition

A complete bipartite graph G:=(V_1 + V_2, E) is a bipartite graph such that for any two vertices v_1 in V_1 and v_2 in V_2 v_1 v_2 is an edge in G. The complete bipartite graph with partitions of size left|V_1right|=m and left|V_2right|=n, is denoted K_{m,n}.

Examples

  • For any k, K_{1,k} is called a star.
  • The graph K_{1,3} is called a claw.

Properties

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