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"...

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...

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

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...

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

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...

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...

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

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;...

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...

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

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...

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...

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...

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}}}}...

{\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...

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

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 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...