GraphTheory
IsBiregular
test if graph is biregular
Calling Sequence
Parameters
Options
Description
Examples
Compatibility
IsBiregular(G)
IsBiregular(G, P)
G
-
graph
P
name
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.
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 non-negative integers D1 and D2 such that every vertex in V1 has degree D1 and every vertex in V2 has degree D2.
with⁡GraphTheory:
K32 ≔ CompleteGraph⁡3,2
K32≔Graph 1: an undirected graph with 5 vertices and 6 edge(s)
IsBiregular⁡K32,'partition'
true,1,2,3,4,5
DrawGraph⁡K32,style=bipartite
AdjacencyMatrix⁡K32
0001100011000111110011100
G ≔ CycleGraph⁡5
G≔Graph 2: an undirected graph with 5 vertices and 5 edge(s)
IsBiregular⁡G
false
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
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