In graph theory, the hypercube graph Q n {\displaystyle Q_{n}} is the edge graph of the n {\displaystyle n} -dimensional hypercube, that is, it is the...

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...

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

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

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...

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

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

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

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

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...

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...

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

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...

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;...

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...

edge graph of the n {\displaystyle n} -dimensional hypercube (including square and cube). Its distance-two graph is known as the halved cube graph and...

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

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...

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect...

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...

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

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...

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...

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...

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}}}}...

bipartite graph K p , q {\displaystyle K_{p,q}} ,then t ( G ) = p q − 1 q p − 1 {\displaystyle t(G)=p^{q-1}q^{p-1}} . For the n-dimensional hypercube graph Q...

product of two hypercube graphs is another hypercube: Qi□Qj = Qi+j. The Cartesian product of two median graphs is another median graph. The graph of vertices...