Examples of using Levi graph in English and their translations into Russian
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Its Levi graph is the Tutte-Coxeter graph. .
The Ljubljana graph is the Levi graph of this configuration.
For every Levi graph, there is an equivalent hypergraph, and vice versa.
The Ljubljana graph on 112 vertices is the Levi graph of the Ljubljana configuration.
The Levi graph of the double six may be obtained by replacing each edge of the crown graph by a two-edge path.
The Tutte eight-cage is the Levi graph of the Cremona-Richmond configuration.
The Levi graph of the Fano plane is the Heawood graph, in which the triangles of the Fano plane are represented by 6-cycles.
That is, the girth of the corresponding bipartite graph(the Levi graph of the configuration) must be at least six.
The Ljubljana graph is the Levi graph of the Ljubljana configuration, a quadrangle-free configuration with 56 lines and 56 points.
Conversely any bipartite graph with girth at least six can be viewed as the Levi graph of an abstract incidence structure.
The Pappus graph is the Levi graph of the Pappus configuration, composed of 9 points and 9 lines.
Each incidence structure C corresponds to a bipartite graph called the Levi graph or incidence graph of the structure.
The Desargues graph is the Levi graph of the Desargues configuration, composed of 10 points and 10 lines.
A closely related configuration, the Möbius-Kantor configuration formed by two mutually inscribed quadrilaterals, has the Möbius-Kantor graph, a subgraph of Q4, as its Levi graph.
It is bipartite, and can be constructed as the Levi graph of the generalized quadrangle W2 known as the Cremona-Richmond configuration.
The Levi graph of a system of points and lines usually has girth at least six: Any 4-cycles would correspond to two lines through the same two points.
However, a combinatorial metric does exist in the corresponding incidence graph( Levi graph), namely the length of the shortest path between two vertices in this bipartite graph. .
The Gray graph is the Levi graph of a configuration that can be realized in R3 as a 3×3×3 grid of 27 points and the 27 orthogonal lines through them.
In the mathematical field of graph theory, the Pappus graph is a bipartite 3-regular undirected graph with 18 vertices and 27 edges,formed as the Levi graph of the Pappus configuration.
The four-dimensional hypercube graph Q4 is the Levi graph of the Möbius configuration formed by the points and planes of two mutually incident tetrahedra.
This construction generalizes(Bouwer 1972)to any dimension n≥ 3, yielding an n-valent Levi graph with algebraic properties similar to those of the Gray graph. .
The Levi graph of the Desargues configuration, a graph having one vertex for each point or line in the configuration, is known as the Desargues graph. .
In 1950, H. S. M. Coxeter cited the graph a second time,giving the Hamiltonian representation used to illustrate this article and describing it as the Levi graph of a projective configuration discovered by Zacharias.
The Levi graph of the Möbius configuration has 16 vertices, one for each point or plane of the configuration, with an edge for every incident point-plane pair.
The Desargues graph, a 20-vertex bipartite symmetric cubic graph, is so called because it can be interpreted as the Levi graph of the Desargues configuration, with a vertex for each point and line of the configuration and an edge for every incident point-line pair.
For instance, the Levi graph of the Fano plane gives rise to the Heawood graph, a bipartite graph with seven vertices on each side, 21 edges, and no 4-cycles, showing that z(7; 2)≥ 21.
Projective geometries Moufang polygon Schläfli double six Reye configuration Cremona-Richmond configuration Kummer configuration Klein configuration Non-Desarguesian planes Combinatorial designs Finite geometry Intersection theorem Levi graph As, for example, L. Storme does in his chapter on Finite Geometry in Colbourn& Dinitz 2007, pg.
The Möbius-Kantor graph is the Levi graph of the Möbius-Kantor configuration, a system of 8 points and 8 lines that cannot be realized by straight lines in the Euclidean plane.
As any bipartite graph is two colorable, the Levi graph can be given a black and white vertex coloring, where black vertices correspond to points and white vertices correspond to lines of C. The edges of this graph correspond to the flags(incident point/line pairs) of the incidence structure.