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Calling Sequence
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LCFGraph(jumps, exp)
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Parameters
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jumps
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-
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list of integers
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exp
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-
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positive integer
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Description
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•
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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.
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Note that the LCF encoding of a particular graph need not be unique.
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List of LCF graphs
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Name
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Vertices
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Edges
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LCF encoding
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Bidiakis cube
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12
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18
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[-6,4,-4], 4
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Duerer graph
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12
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18
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[-4,5,2,-4,-2,5,-5,2,4,-2,-5,4]
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Franklin graph
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12
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18
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[-5,-3,3,5], 3
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Frucht graph
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12
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18
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[-5,-2,-4,2,5,-2,2,5,-2,-5,4,2], 1
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truncated tetrahedron graph
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12
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18
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[2,6,-2], 4
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Moebius-Kantor graph
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16
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24
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[5,-5], 8
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Pappus graph
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18
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27
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[5,7,-7,7,-7,-5], 3
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Desargues graph
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20
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30
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[-9,5,-5,9], 5
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truncated cube graph
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24
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36
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[2,9,-2,2,-9,-2], 4
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truncated octahedron graph
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24
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36
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[3,-7,7,-3], 6
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Nauru graph
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24
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36
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[5,-9,7,-7,9,-5], 4
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McGee graph
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24
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36
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[12,7,-7], 8
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F26A graph
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26
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39
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[-7,7], 13
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(4,6)-cage graph
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26
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52
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[5,9], 13
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Levi graph
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30
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45
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[-13,-9,7,-7,9,13], 5
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Dyck graph
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32
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48
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[-13,5,-5,13], 8
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Gray graph
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54
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81
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[-25,7,-7,13,-13,25], 9
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truncated icosahedron graph
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60
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90
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[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
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Foster graph
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90
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135
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[17,-9,37,-37,9,-17], 15
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Ljubljana graph
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112
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168
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[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
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generalized hexagon graph
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126
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189
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[17,27,-13,-59,-35,35,-11,13,-53,53,-27,21,57,11,-21,-57,59,-17], 7
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Examples
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References
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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.
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