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...

therefore an example of a zonotope. The 1-skeleton of a hypercube is a hypercube graph. A unit hypercube of dimension n {\displaystyle n} is the convex hull...

edges of graphs have exactly two endpoints. hypercube A hypercube graph is a graph formed from the vertices and edges of a geometric hypercube. hypergraph...

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...

the graph known as the cubical graph. It can be constructed by using the Cartesian product of graphs. The cube is the three-dimensional hypercube, a family...

(polyexa) o3o3o3o3o3o4x - hept". Weisstein, Eric W. "Hypercube". MathWorld. Weisstein, Eric W. "Hypercube graph". MathWorld. Olshevsky, George. "Measure polytope"...

other in the hypercube graph. That is, it is the half-square of the hypercube. This connectivity pattern produces two isomorphic graphs, disconnected...

finite graphs that contains all graphs in F; for instance, every finite tree is a subgraph of a sufficiently large hypercube graph so a hypercube can be...

distance graphs include the cactus graphs, the matchstick graphs and penny graphs, and the hypercube graphs. The generalized Petersen graphs are non-strict...

its origin in number theory. Mathematically they are similar to the hypercube graphs, but with a Fibonacci number of vertices. Fibonacci cubes were first...

a hypercube. A parallel computing cluster or multi-core processor is often connected in regular interconnection network such as a de Bruijn graph, a...

cube graph (the 5-regular Clebsch graph) may be constructed by adding edges between opposite pairs of vertices in a 4-dimensional hypercube graph. (In...

4} knight's graph is the same as the four-dimensional hypercube graph. King's graph Queen's graph Rook's graph Bishop's graph Lattice graph Averbach, Bonnie;...

longest possible induced path in an n {\displaystyle n} -dimensional hypercube graph? Sumner's conjecture: does every ( 2 n − 2 ) {\displaystyle (2n-2)}...

dictionary. In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just...

In graph theory, the cube-connected cycles is an undirected cubic graph, formed by replacing each vertex of a hypercube graph by a cycle. It was introduced...

sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem. Similarly, an induced cycle...

In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct...

Levi graph of the Cremona–Richmond configuration. It is also known as the (3,8)-cage, and is 3-regular with 30 vertices. The four-dimensional hypercube graph...

lengths. Hypercube graphs exhibit a similar phenomenon to cycle graphs. The two- and three-dimensional hypercube graphs (the 4-cycle and the graph of a cube...

In graph theory, a partial cube is a graph that is an isometric subgraph of a hypercube. In other words, a partial cube can be identified with a subgraph...

bipartite graphs are the crown graphs, formed from complete bipartite graphs by removing the edges of a perfect matching. Hypercube graphs, partial cubes...

{\displaystyle \varphi (S_{k})=\lfloor (k-1)/2\rfloor +1} . For the hypercube graph Q n {\displaystyle Q_{n}} on 2 n {\displaystyle 2^{n}} vertices the...

possible to define median graphs as the solution sets of 2-satisfiability problems, as the retracts of hypercubes, as the graphs of finite median algebras...

snake for each n-dimensional hypercube graph? More unsolved problems in mathematics The snake-in-the-box problem in graph theory and computer science deals...

In graph theory and computational complexity theory, a Frankl–Rödl graph is a graph defined by connecting pairs of vertices of a hypercube that are at...

within a constant factor. The achromatic number of an n-dimensional hypercube graph is known to be proportional to n 2 n {\displaystyle {\sqrt {n2^{n}}}}...

dimensions gives the hypercube graphs (with 2n vertices and degree n). Similarly extension of the octahedron to n dimensions gives the graphs of the cross-polytopes...

In graph theory, Kuratowski's theorem is a mathematical forbidden graph characterization of planar graphs, named after Kazimierz Kuratowski. It states...

in 1963, it is cospectral to the hypercube graph Q4. The Hoffman graph has many common properties with the hypercube Q4—both are Hamiltonian and have...