K n, m . Complete bipartite graph whose partitions of the set of vertices satisfy that V 1 = n and V 2 = m respectively and that all the vertices of V 1 have edges to all of V 2 .
Definition
A formal definition of K n, m would be that being K n, m = <V 1 UV 2 , A> , where V 1 and V 2 are the two partitions of the set of vertices and A is the collection of edges; If | V 1 | = n , | V 2 | = m and A = V 1 xV 2 then K n, m is a complete bipartite graph of order n and m .
Unlike a common bipartite graph, the set of edges is a nonzero subset of V 1 xV 2 .
Special cases
We know of a complete graph case that is, in turn, a complete bipartite graph; which is also the simplest possible case. K 2 = K 1,1 .
Also one of the Kuratowski graphs is a complete bipartite graph; used in the formal definition of Polish mathematician Kazimierz Kuratowski of planar graph . K 3.3 .
