LCF notation

The Nauru graph[1] has LCF notation [5, –9, 7, –7, 9, –5]4.

In the mathematical field of graph theory, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle.[2][3] The cycle itself includes two out of the three adjacencies for each vertex, and the LCF notation specifies how far along the cycle each vertex's third neighbor is. A single graph may have multiple different representations in LCF notation.

  1. ^ Eppstein, D., The many faces of the Nauru graph, 2007.
  2. ^ Pisanski, Tomaž; Servatius, Brigitte (2013), "2.3.2 Cubic graphs and LCF notation", Configurations from a Graphical Viewpoint, Springer, p. 32, ISBN 9780817683641.
  3. ^ Frucht, R. (1976), "A canonical representation of trivalent Hamiltonian graphs", Journal of Graph Theory, 1 (1): 45–60, doi:10.1002/jgt.3190010111, MR 0463029.