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GraphTheory

  

IsBiregular

 

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 D[2].

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