test if graph is biregular
The options argument can contain one or more of the options shown below.
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 nonnegative integers D1 and D2 such that every vertex in V1 has degree D1 and every vertex in V2 has degree D2.
K32≔Graph 1: an undirected unweighted graph with 5 vertices and 6 edge(s)
G≔Graph 2: an undirected unweighted graph with 5 vertices and 5 edge(s)
The GraphTheory[IsBiregular] command was introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
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