LCF notation

The basic form of the LCF notation is just the sequence of these numbers of positions, starting from an arbitrarily chosen vertex and written in square brackets.

Entries congruent modulo N to 0, 1, or N − 1 do not appear in this sequence of numbers,[4] because they would correspond either to a loop or multiple adjacency, neither of which are permitted in simple graphs.

For example, the Nauru graph,[1] shown on the right, has four repetitions of the same six offsets, and can be represented by the LCF notation [5, −9, 7, −7, 9, −5]4.

A single graph may have multiple different LCF notations, depending on the choices of Hamiltonian cycle and starting vertex.

[6] A more complex extended version of LCF notation was provided by Coxeter, Frucht, and Powers in later work.