Editing Bipartite graph (section)

===Degree===
For a vertex, the number of adjacent vertices is called the [[degree (graph theory)|degree]] of the vertex and is denoted <math>\deg v</math>. The [[degree sum formula]] for a bipartite graph states that<ref>{{citation|title=Combinatorial Problems and Exercises|first=László|last=Lovász|author-link=László Lovász|edition=2nd|publisher=Elsevier|year=2014|isbn=9780080933092|page=281|url=https://books.google.com/books?id=wvHiBQAAQBAJ&pg=PA281}}</ref>
:<math>\sum_{v \in V} \deg v = \sum_{u \in U} \deg u = |E|\, .</math>

The degree sequence of a bipartite graph is the pair of lists each containing the degrees of the two parts <math>U</math> and <math>V</math>. For example, the complete bipartite graph ''K''<sub>3,5</sub> has degree sequence <math>(5,5,5), (3,3,3,3,3)</math>. [[Graph isomorphism|Isomorphic]] bipartite graphs have the same degree sequence. However, the degree sequence does not, in general, uniquely identify a bipartite graph; in some cases, non-isomorphic bipartite graphs may have the same degree sequence.

The [[bipartite realization problem]] is the problem of finding a simple bipartite graph with the degree sequence being two given lists of natural numbers. (Trailing zeros may be ignored since they are trivially realized by adding an appropriate number of isolated vertices to the digraph.)