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GraphTheory

  

IsSplitGraph

  

test if graph is a split graph

 

Calling Sequence

Parameters

Options

Description

Definition

Examples

Compatibility

Calling Sequence

IsSplitGraph(G,opts)

Parameters

G

-

graph

opts

-

(optional) equation of the form decomposition=true or decomposition=false

Options

• 

decomposition : keyword option of the form decomposition=true or decomposition=false. This specifies whether the decomposition into a maximum clique and an independent set should be returned when the graph is a split graph. The default is false.

Description

• 

The IsSplitGraph(G) command returns true if G is a split graph and false otherwise.

Definition

• 

An undirected graph G is a split graph if its vertices can be partitioned into a clique and an independent set. The partition is in general not unique. Split graphs are closed under complement.

Examples

withGraphTheory:

KGraph5,1,2,1,3,2,3,2,4,3,4,4,5

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

(1)

IsSplitGraphK

true

(2)

IsSplitGraphK,decomposition

true,2,3,4,1,5

(3)

PPathGraph4

PGraph 2: an undirected unweighted graph with 4 vertices and 3 edge(s)

(4)

IsSplitGraphP

true

(5)

IsSplitGraphP,decomposition

true,2,3,1,4

(6)

GSpecialGraphs:-PetersenGraph

GGraph 3: an undirected unweighted graph with 10 vertices and 15 edge(s)

(7)

IsSplitGraphG

false

(8)

Compatibility

• 

The GraphTheory[IsSplitGraph] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

DegreeSequence

MaximumClique

MaximumIndependentSet