graph_from_lcf: Creating a graph from LCF notation

In igraph: Network Analysis and Visualization

Creating a graph from LCF notation

Description

LCF is short for Lederberg-Coxeter-Frucht, it is a concise notation for 3-regular Hamiltonian graphs. It constists of three parameters, the number of vertices in the graph, a list of shifts giving additional edges to a cycle backbone and another integer giving how many times the shifts should be performed. See https://mathworld.wolfram.com/LCFNotation.html for details.

Usage

graph_from_lcf(shifts, ..., n = NULL, repeats = 1L)

Arguments

shifts	Integer vector, the shifts.
...	These dots are for future extensions and must be empty.
n	Integer, the number of vertices in the graph. If NULL (default), it is set to len(shifts) * repeats.
repeats	Integer constant, how many times to repeat the shifts.

Value

A graph object.

Related documentation in the C library

lcf_vector().

Author(s)

Gabor Csardi [e-mail]

See Also

make_graph() can create arbitrary graphs, see also the other functions on the its manual page for creating special graphs.

Examples

# This is the Franklin graph:
g1 <- graph_from_lcf(shifts = c(5L, -5L), n = 12L, repeats = 6L)
g2 <- make_graph("Franklin")
isomorphic(g1, g2)

igraph documentation built on Feb. 12, 2026, 5:08 p.m.