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Folded cube graph information


Folded cube graph
The dimension-5 folded cube graph (i.e, the Clebsch graph).
Vertices
Edges
Diameter
Chromatic number
PropertiesRegular
Hamiltonian
Distance-transitive.
Table of graphs and parameters

In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects opposite pairs of hypercube vertices.

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Folded cube graph

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In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects opposite pairs...

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Hypercube graph

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In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q3...

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Clebsch graph

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Clebsch. The 40-edge variant is the dimension-5 folded cube graph; it is also known as the Greenwood–Gleason graph after the work of Robert E. Greenwood and...

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Glossary of graph theory

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vertices and edges of a cube. 2.  Hypercube graph, a higher-dimensional generalization of the cube graph. 3.  Folded cube graph, formed from a hypercube...

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Halved cube graph

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In graph theory, the halved cube graph or half cube graph of dimension n is the graph of the demihypercube, formed by connecting pairs of vertices at distance...

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Cube

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the cube (the vertices and edges) forms a graph with 8 vertices and 12 edges, called the cube graph. It is a special case of the hypercube graph. It is...

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Regular dodecahedron

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a graph. It is one of 5 Platonic graphs, each a skeleton of its Platonic solid. This graph can also be constructed as the generalized Petersen graph G(10...

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Snub cube

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snub cube is second in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n. In graph theory, a snub cubical graph is the graph of vertices...

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Menger sponge

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cube. Divide every face of the cube into nine squares, like a Rubik's Cube. This sub-divides the cube into 27 smaller cubes. Remove the smaller cube in...

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Regular icosahedron

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regular faces to each of its pentagonal faces, or by putting points onto the cube. The resulting polyhedron has 20 equilateral triangles as its faces, 30 edges...

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Truncated cube

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cubic Archimedean graph. Spinning truncated cube Cube-connected cycles, a family of graphs that includes the skeleton of the truncated cube B. M. Stewart...

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Rhombicuboctahedron

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is an Archimedean solid. The polyhedron has octahedral symmetry, like the cube and octahedron. Its dual is called the deltoidal icositetrahedron or trapezoidal...

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Truncated cuboctahedron

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zero-symmetric and cubic Archimedean graph. Wikimedia Commons has media related to Truncated cuboctahedron. Cube Cuboctahedron Octahedron Truncated icosidodecahedron...

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Tesseract

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originally spelled the word as tessaract. As a regular polytope with three cubes folded together around every edge, it has Schläfli symbol {4,3,3} with hyperoctahedral...

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Cuboctahedron

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constructed as the line graph of the cube. It has 12 vertices and 24 edges, is locally linear, and is a quartic Archimedean graph. Icosidodecahedron Pseudocuboctahedron...

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Polycube

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polycube can be visualized by means of a "dual graph" that has a vertex for each cube and an edge for each two cubes that share a square. This is different from...

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Odd graph

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include the odd graphs and the folded cube graphs. Although the Petersen graph has been known since 1898, its definition as an odd graph dates to the work...

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Truncated tetrahedron

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Atlas of Graphs, page=172, C105 An Atlas of Graphs, page 267, truncated tetrahedral graph An Atlas of Graphs, page 130, connected cubic graphs, 12 vertices...

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Truncated octahedron

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in Bonn Rubik's Cube variant model made with Polydron construction set Pyrite crystal Boleite crystal In the mathematical field of graph theory, a truncated...

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Octahedral symmetry

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symmetry group of the cube and octahedron. It is the hyperoctahedral group for n = 3. See also the isometries of the cube. With the 4-fold axes as coordinate...

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Forbidden graph characterization

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In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to...

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List of unsolved problems in mathematics

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combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory...

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Tetrahedron

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the cube. The cube can be dissected into six such 3-orthoschemes four different ways, with all six surrounding the same √3 cube diagonal. The cube can...

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Cubic equation

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four coefficients, the four basic arithmetic operations, square roots and cube roots. (This is also true of quadratic (second-degree) and quartic (fourth-degree)...

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