LCF_graph#

LCF_graph(n, shift_list, repeats, create_using=None)[source]#

Return the cubic graph specified in LCF notation.

LCF notation (LCF=Lederberg-Coxeter-Fruchte) is a compressed notation used in the generation of various cubic Hamiltonian graphs of high symmetry. See, for example, dodecahedral_graph, desargues_graph, heawood_graph and pappus_graph below.

n (number of nodes): The starting graph is the n-cycle with nodes 0,…,n-1. (The null graph is returned if n < 0.)

shift_list = [s1,s2,..,sk], a list of integer shifts mod n,

repeats: 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.

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

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

>>> G = nx.LCF_graph(6, [3, -3], 3)

The Heawood graph

>>> G = nx.LCF_graph(14, [5, -5], 7)

See http://mathworld.wolfram.com/LCFNotation.html for a description and references.