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complete bipartite graph (Definition)

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}$:

$\displaystyle \begin{xy} *!C\xybox{ \xymatrix{ & C \ A \ar@{-}[ur] \ar@{-}[r]... ...[uuur] \ar@{-}[uur] \ar@{-}[ur] \ar@{-}[r] \ar@{-}[dr] & F \ & G } } \end{xy}$

$ K_{3,3}$:

$\displaystyle \begin{xy} *!C\xybox{ \xymatrix{ A \ar@{-}[r] \ar@{-}[dr] \ar@{-}... ...}[r] \ar@{-}[dr] & E \ C \ar@{-}[uur] \ar@{-}[ur] \ar@{-}[r] & F } } \end{xy}$



"complete bipartite graph" is owned by yark. [ full author list (2) | owner history (1) ]
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Cross-references: bipartite, implies, adjacent, vertex, vertices, graph
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This is version 4 of complete bipartite graph, born on 2002-02-03, modified 2006-01-24.
Object id is 1784, canonical name is CompleteBipartiteGraph.
Accessed 4476 times total.

Classification:
AMS MSC05C15 (Combinatorics :: Graph theory :: Coloring of graphs and hypergraphs)

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