GraphTheory[SpecialGraphs]
LCFGraph
construct LCF graph
Calling Sequence
Parameters
Description
List of LCF graphs
Examples
References
LCFGraph(jumps, exp)
jumps
-
list of integers
exp
positive integer
A graph represented by the LCF notation jumps^exp. LCF (Lederberg-Coxeter-Frucht) notation is a convenient notation for the representation of cubic graphs which contain a Hamiltonian cycle.
Note that the LCF encoding of a particular graph need not be unique.
Name
Vertices
Edges
LCF encoding
Bidiakis cube
12
18
[-6,4,-4], 4
Duerer graph
[-4,5,2,-4,-2,5,-5,2,4,-2,-5,4]
Franklin graph
[-5,-3,3,5], 3
Frucht graph
[-5,-2,-4,2,5,-2,2,5,-2,-5,4,2], 1
truncated tetrahedron graph
[2,6,-2], 4
Moebius-Kantor graph
16
24
[5,-5], 8
Pappus graph
27
[5,7,-7,7,-7,-5], 3
Desargues graph
20
30
[-9,5,-5,9], 5
truncated cube graph
36
[2,9,-2,2,-9,-2], 4
truncated octahedron graph
[3,-7,7,-3], 6
Nauru graph
[5,-9,7,-7,9,-5], 4
McGee graph
[12,7,-7], 8
F26A graph
26
39
[-7,7], 13
(4,6)-cage graph
52
[5,9], 13
Levi graph
45
[-13,-9,7,-7,9,13], 5
Dyck graph
32
48
[-13,5,-5,13], 8
Gray graph
54
81
[-25,7,-7,13,-13,25], 9
truncated icosahedron graph
60
90
[30,-2,2,21,-2,2,12,-2,2,-12,-2,2,-21,-2,2,30,-2,2,-12,-2,2,21,-2,2,-21,-2,2,12,-2,2], 2
Foster graph
135
[17,-9,37,-37,9,-17], 15
Ljubljana graph
112
168
[47,-23,-31,39,25,-21,-31,-41,25,15,29,-41,-19,15,-49,33,39,-35,-21,17,-33,49,41,31,-15,-29,41,31,-15,-25,21,31,-51,-25,23,9,-17,51,35,-29,21,-51,-39,33,-9,-51,51,-47,-33,19,51,-21,29,21,-31,-39], 2
generalized hexagon graph
126
189
[17,27,-13,-59,-35,35,-11,13,-53,53,-27,21,57,11,-21,-57,59,-17], 7
with⁡GraphTheory:with⁡SpecialGraphs:
G≔LCFGraph⁡3,−3,4
G≔Graph 1: an undirected graph with 8 vertices and 12 edges
DrawGraph⁡G
H≔HypercubeGraph⁡3
H≔Graph 2: an undirected graph with 8 vertices and 12 edges
DrawGraph⁡H
Pisanski, Tomaž; Servatius, Brigitte (2013), "2.3.2 Cubic graphs and LCF notation", Configurations from a Graphical Viewpoint, Birkhäuser Advanced Texts Basler Lehrbücher, p.32.
"LCF Notation", Wikipedia. http://en.wikipedia.org/wiki/LCF_notation
See Also
SpecialGraphs
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