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Generation of all SCT (simple, connected, 2-connected) graphs on small numbers of vertices -- generating all SCT graphs on n vertices

Using the NautyGraphs package, we generate the list of isomorphism classes of the SCT (simple, connected, 2-connected) graphs with a fixed number of vertices.

i1 : needsPackage "Oscillators"

o1 = Oscillators

o1 : Package
i2 : needsPackage "NautyGraphs"

o2 = NautyGraphs

o2 : Package
i3 : Gstrs = generateGraphs(5, OnlyConnected => true, MinDegree => 2);
i4 : #Gstrs == 11

o4 = true
i5 : Gstrs = generateGraphs(6, OnlyConnected => true, MinDegree => 2);
i6 : #Gstrs == 61

o6 = true
i7 : Gstrs = generateGraphs(7, OnlyConnected => true, MinDegree => 2);
i8 : #Gstrs == 507

o8 = true
i9 : Gstrs = generateGraphs(8, OnlyConnected => true, MinDegree => 2);
i10 : #Gstrs == 7442

o10 = true
i11 : Gstrs = generateGraphs(9, OnlyConnected => true, MinDegree => 2);
i12 : #Gstrs == 197772

o12 = true

Here is a simple table with all of these numbers.

i13 : netList for n from 5 to 9 list {n, #generateGraphs(n, OnlyConnected => true, MinDegree => 2)}

      +-+------+
o13 = |5|11    |
      +-+------+
      |6|61    |
      +-+------+
      |7|507   |
      +-+------+
      |8|7442  |
      +-+------+
      |9|197772|
      +-+------+

The source of this document is in Oscillators/Documentation.m2:708:0.