Bipartite graph

A bipartite graph, or bigraph, is a graph whose vertices can be partitioned into \(2\) disjoint sets such that every edge in the graph connects a vertex in one set to a vertex in the other set. In other words, there are no edges between vertices in the same set.

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Complete bipartite graph

A complete bipartite graph is a bipartite graph where every vertex in one set is connected to every vertex in the other set. Essentially, it has as many edges as the definition of a bipartite graph will allow. The symbol \(K_{n,m}\) denotes the complete bigraph with \(n\) vertices in one set and \(m\) vertices in the other set.

Naturally, \(K_{n,m}\) has \(n + m\) vertices and \(n \times m\) edges. (Remember, each of the \(n\) vertices in one set is connected to each of the \(m\) vertices in the other set.)

When one set in a complete bipartite graph consists of exactly \(1\) vertex, the resulting graph is called a star.

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