Creating a graph from LCF notation

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 http://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.

See also

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

Author

Gabor Csardi csardi.gabor@gmail.com

Related documentation in the C library

lcf_vector().

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)
#> [1] TRUE