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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.".
- LCF_notation thumbnail Nauru_graph_LCF.svg?width=300.
- LCF_notation wikiPageExternalLink 1703449.
- LCF_notation wikiPageExternalLink mathgames_12_29_03.html.
- LCF_notation wikiPageID "24186720".
- LCF_notation wikiPageRevisionID "546752103".
- LCF_notation hasPhotoCollection LCF_notation.
- LCF_notation title "LCF Notation".
- LCF_notation urlname "LCFNotation".
- LCF_notation subject Category:Graph_description_languages.
- LCF_notation subject Category:Hamiltonian_paths_and_cycles.
- LCF_notation type Abstraction100002137.
- LCF_notation type Act100030358.
- LCF_notation type Action100037396.
- LCF_notation type Communication100033020.
- LCF_notation type Course100038262.
- LCF_notation type Event100029378.
- LCF_notation type GraphDescriptionLanguages.
- LCF_notation type HamiltonianPathsAndCycles.
- LCF_notation type Language106282651.
- LCF_notation type PsychologicalFeature100023100.
- LCF_notation type Way100415676.
- LCF_notation type YagoPermanentlyLocatedEntity.
- 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 label "LCF-Notation".
- LCF_notation label "Notation LCF".
- LCF_notation label "Notazione LCF".
- LCF_notation sameAs LCF-Notation.
- LCF_notation sameAs Notation_LCF.
- LCF_notation sameAs Notazione_LCF.
- LCF_notation sameAs m.07k89_0.
- LCF_notation sameAs Q1797915.
- LCF_notation sameAs Q1797915.
- LCF_notation sameAs LCF_notation.
- LCF_notation wasDerivedFrom LCF_notation?oldid=546752103.
- LCF_notation depiction Nauru_graph_LCF.svg.
- LCF_notation isPrimaryTopicOf LCF_notation.
