# complete bipartite graph

The complete bipartite graph $K_{n,m}$ is a graph with two sets of vertices, one with $n$ members and one with $m$, such that each vertex in one set is adjacent to every vertex in the other set and to no vertex in its own set. As the name implies, $K_{n,m}$ is bipartite.

Examples of complete bipartite graphs:

$K_{2,5}$:

 $\xymatrix{&C\\ A\ar@{-}[ur]\ar@{-}[r]\ar@{-}[dr]\ar@{-}[ddr]\ar@{-}[dddr]&D\\ &E\\ B\ar@{-}[uuur]\ar@{-}[uur]\ar@{-}[ur]\ar@{-}[r]\ar@{-}[dr]&F\\ &G}$

$K_{3,3}$:

 $\xymatrix{A\ar@{-}[r]\ar@{-}[dr]\ar@{-}[ddr]&D\\ B\ar@{-}[ur]\ar@{-}[r]\ar@{-}[dr]&E\\ C\ar@{-}[uur]\ar@{-}[ur]\ar@{-}[r]&F}$
Title complete bipartite graph CompleteBipartiteGraph 2013-03-22 12:17:13 2013-03-22 12:17:13 yark (2760) yark (2760) 7 yark (2760) Definition msc 05C15