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- LCF_notation abstract "In combinatorial mathematics, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by Coxeter and Frucht, for the representation of cubic graphs that are Hamiltonian. Since the graphs are Hamiltonian, the vertices can be arranged in a cycle, which accounts for two edges per vertex. The third edge from each vertex can then be described by how many positions clockwise (positive) or counter-clockwise (negative) it leads. Often the pattern repeats, which is indicated by a superscript in the notation. For example, the Nauru graph, shown on the right, has LCF notation [5, −9, 7, −7, 9, −5]4. Graphs may have different LCF notations, depending on precisely how the vertices are arranged.The numbers between the square brackets are interpreted modulo N, where N is the number of vertices. Entries equal (modulo N) to 0, 1, and N−1 are not permitted, since they do not correspond to valid third edges.LCF notation is useful in publishing concise descriptions of Hamiltonian cubic graphs, such as the examples below. In addition, some software packages for manipulating graphs include utilities for creating a graph from its LCF notation.If a graph is represented by LCF notation, it is straightforward to test whether the graph is bipartite: this is true if and only if all of the offsets in the LCF notation are odd.".
- LCF_notation thumbnail Nauru_graph_LCF.svg?width=300.
- LCF_notation wikiPageExternalLink mathgames_12_29_03.html.
- LCF_notation wikiPageExternalLink 1703449.
- LCF_notation wikiPageID "24186720".
- LCF_notation wikiPageLength "9281".
- LCF_notation wikiPageOutDegree "45".
- LCF_notation wikiPageRevisionID "642048891".
- LCF_notation wikiPageWikiLink Balaban_10-cage.
- LCF_notation wikiPageWikiLink Balaban_11-cage.
- LCF_notation wikiPageWikiLink Bidiakis_cube.
- LCF_notation wikiPageWikiLink Biggs-Smith_graph.
- LCF_notation wikiPageWikiLink Biggs–Smith_graph.
- LCF_notation wikiPageWikiLink Bipartite_graph.
- LCF_notation wikiPageWikiLink Category:Graph_description_languages.
- LCF_notation wikiPageWikiLink Category:Hamiltonian_paths_and_cycles.
- LCF_notation wikiPageWikiLink Circular_layout.
- LCF_notation wikiPageWikiLink Combinatorics.
- LCF_notation wikiPageWikiLink Cube.
- LCF_notation wikiPageWikiLink Cubic_graph.
- LCF_notation wikiPageWikiLink D3.js.
- LCF_notation wikiPageWikiLink D3js.
- LCF_notation wikiPageWikiLink Desargues_graph.
- LCF_notation wikiPageWikiLink Dodecahedron.
- LCF_notation wikiPageWikiLink Dyck_graph.
- LCF_notation wikiPageWikiLink F26A_graph.
- LCF_notation wikiPageWikiLink Foster_graph.
- LCF_notation wikiPageWikiLink Franklin_graph.
- LCF_notation wikiPageWikiLink Frucht_graph.
- LCF_notation wikiPageWikiLink Gray_graph.
- LCF_notation wikiPageWikiLink Hamiltonian_path.
- LCF_notation wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- LCF_notation wikiPageWikiLink Harries_graph.
- LCF_notation wikiPageWikiLink Harries–Wong_graph.
- LCF_notation wikiPageWikiLink Heawood_graph.
- LCF_notation wikiPageWikiLink Hypercube_graph.
- LCF_notation wikiPageWikiLink Joshua_Lederberg.
- LCF_notation wikiPageWikiLink Ljubljana_graph.
- LCF_notation wikiPageWikiLink McGee_graph.
- LCF_notation wikiPageWikiLink Modular_arithmetic.
- LCF_notation wikiPageWikiLink Möbius–Kantor_graph.
- LCF_notation wikiPageWikiLink Nauru_graph.
- LCF_notation wikiPageWikiLink Octahedron.
- LCF_notation wikiPageWikiLink Pappus_graph.
- LCF_notation wikiPageWikiLink Robert_Frucht.
- LCF_notation wikiPageWikiLink Tetrahedron.
- LCF_notation wikiPageWikiLink Three_utilities_problem.
- LCF_notation wikiPageWikiLink Tutte_12-cage.
- LCF_notation wikiPageWikiLink Tutte–Coxeter_graph.
- LCF_notation wikiPageWikiLink Wagner_graph.
- LCF_notation wikiPageWikiLink Water,_gas,_and_electricity.
- LCF_notation wikiPageWikiLink Zero-symmetric_graph.
- LCF_notation wikiPageWikiLink File:Nauru_graph_LCF.svg.
- LCF_notation wikiPageWikiLinkText "LCF notation".
- LCF_notation hasPhotoCollection LCF_notation.
- LCF_notation title "LCF Notation".
- LCF_notation urlname "LCFNotation".
- LCF_notation wikiPageUsesTemplate Template:Citation.
- LCF_notation wikiPageUsesTemplate Template:For.
- LCF_notation wikiPageUsesTemplate Template:MathWorld.
- LCF_notation wikiPageUsesTemplate Template:Reflist.
- LCF_notation subject Category:Graph_description_languages.
- LCF_notation subject Category:Hamiltonian_paths_and_cycles.
- LCF_notation hypernym Notation.
- LCF_notation type Language.
- LCF_notation type Software.
- LCF_notation type Language.
- LCF_notation type Object.
- LCF_notation comment "In combinatorial mathematics, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by Coxeter and Frucht, for the representation of cubic graphs that are Hamiltonian. Since the graphs are Hamiltonian, the vertices can be arranged in a cycle, which accounts for two edges per vertex. The third edge from each vertex can then be described by how many positions clockwise (positive) or counter-clockwise (negative) it leads.".
- LCF_notation label "LCF notation".
- LCF_notation sameAs LCF-Notation.
- LCF_notation sameAs Notation_LCF.
- LCF_notation sameAs Notazione_LCF.
- LCF_notation sameAs m.07k89_0.
- LCF_notation sameAs LCF-нотация.
- LCF_notation sameAs Q1797915.
- LCF_notation sameAs Q1797915.
- LCF_notation wasDerivedFrom LCF_notation?oldid=642048891.
- LCF_notation depiction Nauru_graph_LCF.svg.
- LCF_notation isPrimaryTopicOf LCF_notation.