graph_tool.collection.LCF_graph#

graph_tool.collection.LCF_graph(n, shift_list, repeats)[source]#

Returns the cubic graph specified in LCF notation.

Parameters:
nint

Number of nodes. The starting graph is the n-cycle with nodes \(0,\dots,n-1\). (The empty graph is returned if n < 0.)

shift_listlist

A list \([s_1,s_2,\dots,s_k]\) of integer shifts \(\mod n\).

repeatsint

Integer specifying the number of times that shifts in shift_list are successively applied to each v_current in the n-cycle to generate an edge between v_current and v_current + shift mod n.

Notes

The Lederberg-Coxeter-Fruchte (LCF) notation is a compressed notation used in the generation of various cubic Hamiltonian graphs of high symmetry [LCF].

See, for example, dodecahedral_graph(), desargues_graph(), heawood_graph() and pappus_graph().

For v1 cycling through the n-cycle a total of k * repeats with shift cycling through shiftlist repeats times connect v1 with v1 + shift mod n.

References

Examples

The utility graph \(K_{3,3}\)

>>> g = gt.LCF_graph(6, [3, -3], 3)

The Heawood graph

>>> g = gt.LCF_graph(14, [5, -5], 7)