construct cage graph
Named Cage Graphs
degree of graph
girth of graph
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.
Several notable cage graphs have been assigned names and can be individually accessed under these names within the SpecialGraphs subpackage. These include:
(3,10)-cages: Balaban10CageGraph, HarriesGraph, and HarriesWongGraph
(5,5)-cages: FosterCageGraph, MeringerGraph, RobertsonWegnerGraph, and WongGraph
This is the Petersen graph
C ≔ CageGraph⁡3,5
C≔Graph 1: an undirected graph with 10 vertices and 15 edge(s)
A sequence of three 3-regular graphs with girth 10
C3 ≔ CageGraph⁡3,10
C3≔Graph 2: an undirected graph with 70 vertices and 105 edge(s),Graph 3: an undirected graph with 70 vertices and 105 edge(s),Graph 4: an undirected graph with 70 vertices and 105 edge(s)
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