Editing Complete bipartite graph (section)

== Definition ==
A '''complete bipartite graph''' is a graph whose vertices can be partitioned into two subsets {{math|''V''{{sub|1}}}} and {{math|''V''{{sub|2}}}} such that no edge has both endpoints in the same subset, and every possible edge that could connect vertices in different subsets is part of the graph. That is, it is a [[bipartite graph]] {{math|(''V''{{sub|1}}, ''V''{{sub|2}}, ''E'')}} such that for every two vertices {{math|''v''{{sub|1}} ∈ ''V''{{sub|1}}}} and{{math| ''v''{{sub|2}} ∈ ''V''{{sub|2}}}}, {{math|''v''{{sub|1}}''v''{{sub|2}}}} is an edge in {{mvar|E}}. A complete bipartite graph with partitions of size {{math|1={{abs|''V''{{sub|1}}}} = ''m''}} and {{math|1={{abs|''V''{{sub|2}}}} = ''n''}}, is denoted {{math|''K''{{sub|''m'',''n''}}}};<ref name="bm"/><ref name="d"/> every two graphs with the same notation are [[graph isomorphism|isomorphic]].