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GraphTheory

  

IsStronglyRegular

  

test if graph is strongly regular

 

Calling Sequence

Parameters

Options

Description

Definition

Strongly regular graphs in SpecialGraphs

Examples

Compatibility

Calling Sequence

IsStronglyRegular(G,opts)

Parameters

G

-

graph

opts

-

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

Options

• 

parameters : keyword option of the form parameters=true or parameters=false. This specifies whether the parameters [k, lambda, mu] should be returned when the graph is strongly regular. The default is false.

Description

• 

The IsStronglyRegular(G) command returns true if G is a strongly regular graph and false otherwise.

Definition

• 

An undirected graph G is strongly regular if there exist integers k, lambda, and mu such that every vertex has k neighbors and for every pair of vertices (u,v), u and v have exactly lambda neighbors in common if they are themselves adjacent, and exactly mu neighbors in common if they are not.

• 

Note that some parts of this definition may be satisfied trivially, in which a complete graph every pair of vertices is adjacent, so the choice of mu could be arbitrary and therefore mu is undefined.

• 

Any strongly regular graph is regular, but the converse is not true.

Strongly regular graphs in SpecialGraphs

• 

The following are graphs in the SpecialGraphs subpackage which are strongly regular.

Graph

Number of Vertices

k

lambda

mu

Octahedron graph

6

4

2

4

Petersen graph

10

3

0

1

Clebsch graph

16

5

0

2

Shrikhande graph

16

6

2

2

Schlaefli graph

27

16

10

8

Hoffman-Singleton graph

50

7

0

1

Gewirtz graph

56

10

0

2

M22 graph

77

16

0

4

Brouwer-Haemers graph

81

20

1

6

Higman-Sims graph

100

22

0

6

Cameron graph

231

30

9

3

Berlekamp-van Lint-Seidel graph

243

22

1

2

McLaughlin graph

275

112

30

56

Suzuki graph

1782

416

100

96

Examples

withGraphTheory:

withSpecialGraphs:

GGraph1,2,1,3,2,3,3,4

GGraph 1: an undirected unweighted graph with 4 vertices and 4 edge(s)

(1)

DegreeSequenceG

2,2,3,1

(2)

IsStronglyRegularG

false

(3)

PPetersenGraph

PGraph 2: an undirected unweighted graph with 10 vertices and 15 edge(s)

(4)

DegreeSequenceP

3,3,3,3,3,3,3,3,3,3

(5)

IsStronglyRegularP,parameters

true,3,0,1

(6)

DrawGraphP

CClebschGraph

CGraph 3: an undirected unweighted graph with 16 vertices and 40 edge(s)

(7)

IsStronglyRegularC,parameters

true,5,0,2

(8)

DrawGraphC

Compatibility

• 

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

• 

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

See Also

Degree

DegreeSequence

IsRegular