πŸ”₯ LCF notation - Wikipedia

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In combinatorial mathematics, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle. The cycle itself includes two out of the three adjacencies for each vertex, and 1 Description; 2 Applications; 3 Examples; 4 Extended LCF notation; 5.


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In combinatorial mathematics, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle. The cycle itself includes two out of the three adjacencies for each vertex, and 1 Description; 2 Applications; 3 Examples; 4 Extended LCF notation; 5.


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In combinatorial mathematics, LCF notation or LCF code is a notation devised by Joshua Lederberg, and extended by H. S. M. Coxeter and Robert Frucht, for the representation of cubic graphs that contain a Hamiltonian cycle. The cycle itself includes two out of the three adjacencies for each vertex, and 1 Description; 2 Applications; 3 Examples; 4 Extended LCF notation; 5.


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There may exist multiple cages for a given combination of r and g. Moreover, the bounds on the sizes of Moore graphs generalize to cages: any cage with odd girth g must have at least. More precisely,. Any r , g -graph with exactly this many vertices is by definition a Moore graph and therefore automatically a cage. From Wikipedia, the free encyclopedia. It is unlikely that these graphs are themselves cages, but their existence gives an upper bound to the number of vertices needed in a cage. Equivalently, g can be at most proportional to the logarithm of n. Categories : Graph families Regular graphs. Download as PDF Printable version.{/INSERTKEYS}{/PARAGRAPH} The best known lower bounds on g are also logarithmic, but with a smaller constant factor implying that n grows singly exponentially but at a higher rate than the Moore bound. Formally, an r , g -graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. For large values of g , the Moore bound implies that the number n of vertices must grow at least singly exponentially as a function of g. If a Moore graph exists with degree r and girth g , it must be a cage. {PARAGRAPH}{INSERTKEYS}In the mathematical area of graph theory , a cage is a regular graph that has as few vertices as possible for its girth. An r , g -cage is an r , g -graph with the fewest possible number of vertices, among all r , g -graphs. Namespaces Article Talk. Views Read Edit View history. Help Community portal Recent changes Upload file.