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GraphTheory[SpecialGraphs]

  

CageGraph

  

construct cage graph

 

Calling Sequence

Parameters

Description

Named Cage Graphs

Examples

Calling Sequence

CageGraph(K, G)

Parameters

K

-

degree of graph

G

-

girth of graph

Description

• 

The CageGraph(K,G) command creates the (K,G')-cage graph, that is, the smallest K-regular graph(s) with girth G.

• 

If more than one graph meets these criteria, a sequence of graphs is returned.

• 

In the cases where the smallest graph is not known, FAIL is returned.

Named Cage Graphs

• 

Several notable cage graphs have been assigned names and can be individually accessed under these names within the SpecialGraphs subpackage. These include:

• 

(3,5)-cage: PetersenGraph

• 

(3,6)-cage: HeawoodGraph

• 

(3,8)-cage: Tutte8CageGraph

• 

(3,10)-cages: Balaban10CageGraph, HarriesGraph, and HarriesWongGraph

• 

(4,5)-cage: RobertsonGraph

• 

(5,5)-cages: FosterCageGraph, MeringerGraph, RobertsonWegnerGraph, and WongGraph.

• 

(7,5)-cage: HoffmanSingletonGraph

Examples

withGraphTheory:

withSpecialGraphs:

This is the Petersen graph

CCageGraph3,5

C:=Graph 1: an undirected unweighted graph with 10 vertices and 15 edge(s)

(1)

DrawGraphC

A sequence of three 3-regular graphs with girth 10

C3CageGraph3,10

C3:=Graph 2: an undirected unweighted graph with 70 vertices and 105 edge(s),Graph 3: an undirected unweighted graph with 70 vertices and 105 edge(s),Graph 4: an undirected unweighted graph with 70 vertices and 105 edge(s)

(2)

Not known

CageGraph8,11

FAIL

(3)

See Also

Girth

SpecialGraphs

 


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