LCF-Notation

90, [17, -9.37, -37.9, -17 ], 15 an associated LCF notation. In combinatorics as a branch of discrete mathematics is the Lederberg - Coxeter - fruits notation ( short LCF) a compact representation of finite cubic Hamiltonian graphs. The notation goes back to Joshua Lederberg and is extended by HSM Coxeter and Robert fruit. Many programs for manipulating graphs support LCF inputs.

Syntax

Each LCF code has the following form:

This is the number of nodes that are elements of a complete system of residues modulo without the smallest zero ( in other words, all the figures ) and is an iteration parameter, so that. In printed publications to write well.

A method to reverse to calculate a LCF to a graph code can then easily construct. LCF notations to a graph are generally not uniquely determined. They depend on the choice of the start node and the choice of the Hamilton cycle (there will always be at least one has the choice of orientation). Conversely, however, there may be any LCF notation only one to give up to isomorphism, unique graph. If one LCF code together with a plot is, it is convention that node if they are not numbered, along the chosen Hamilton cycle " circular " (exact polygonal) set to the node "at the top " is.

  • Some plots with LCF codes
  • The Wagner graph: 8, [ -4] 8
  • The McGee graph: 24, [ 12.7, -7 ], 8
  • The Franklin graph: 12, [5, -5], 6
  • The Möbius Cantor graph: 16, [5, -5], 8
  • The Franklin graph: ( alternate representation ) 12, [-5, -3,3,5 ], 3
Cubic graph Convention (norm) Wolfram Research Sage (mathematics software)
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