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GraphTheory

  

IsBiregular

  

test if graph is biregular

 

Calling Sequence

Parameters

Options

Description

Examples

Compatibility

Calling Sequence

IsBiregular(G)

IsBiregular(G, P)

Parameters

G

-

graph

Options

  

The options argument can contain one or more of the options shown below.

• 

partition=truefalse

  

If partition=true and G is biregular, two lists of vertices comprising a biregular partition of G are returned. Otherwise a simple Boolean value is returned indicating whether the graph is biregular.

Description

• 

IsBiregular returns true if the graph G is biregular and false otherwise. If a variable name P is specified, then this name is assigned a bipartition of the vertices as a list of lists.

• 

A graph G is biregular if its set of vertices can be partitioned into two sets, V1 and V2, such that every edge in G connects a vertex in V1 to a vertex in V2 and if there exist nonnegative integers D1 and D2 such that every vertex in V1 has degree D1 and every vertex in V2 has degree D2.

Examples

withGraphTheory:

K32CompleteGraph3,2

K32Graph 1: an undirected unweighted graph with 5 vertices and 6 edge(s)

(1)

IsBiregularK32,partition

true,1,2,3,4,5

(2)

DrawGraphK32,style=bipartite

AdjacencyMatrixK32

0001100011000111110011100

(3)

GCycleGraph5

GGraph 2: an undirected unweighted graph with 5 vertices and 5 edge(s)

(4)

IsBiregularG

false

(5)

Compatibility

• 

The GraphTheory[IsBiregular] command was introduced in Maple 2019.

• 

For more information on Maple 2019 changes, see Updates in Maple 2019.

See Also

AdjacencyMatrix

BipartiteMatching

DrawGraph

IsBipartite

IsRegular