Matches in DBpedia 2015-10 for { ?s ?p "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."@en }
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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.".