Symmetric Distance regular Unit distance Hamiltonian Bipartite
Notation
Qn
Table of graphs and parameters
In graph theory, the hypercube graphQn is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube.
Qn has 2n vertices, 2n – 1n edges, and is a regular graph with n edges touching each vertex.
The hypercube graph Qn may also be constructed by creating a vertex for each subset of an n-element set, with two vertices adjacent when their subsets differ in a single element, or by creating a vertex for each n-digit binary number, with two vertices adjacent when their binary representations differ in a single digit. It is the n-fold Cartesian product of the two-vertex complete graph, and may be decomposed into two copies of Qn – 1 connected to each other by a perfect matching.
Hypercube graphs should not be confused with cubic graphs, which are graphs that have exactly three edges touching each vertex. The only hypercube graph Qn that is a cubic graph is the cubical graph Q3.
In graph theory, the hypercubegraph 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 hypercubegraph. A unit hypercube of dimension n {\displaystyle n} is the convex hull...
forms a graph with 8 vertices and 12 edges, called the cube graph. It is a special case of the hypercubegraph. It is one of 5 Platonic graphs, each a...
edges of graphs have exactly two endpoints. hypercube A hypercubegraph is a graph formed from the vertices and edges of a geometric hypercube. hypergraph...
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...
a hypercube. A parallel computing cluster or multi-core processor is often connected in regular interconnection network such as a de Bruijn graph, a...
its origin in number theory. Mathematically they are similar to the hypercubegraphs, but with a Fibonacci number of vertices. Fibonacci cubes were first...
longest possible induced path in an n {\displaystyle n} -dimensional hypercubegraph? 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 hypercubegraph. (In...
In graph theory, a folded cube graph is an undirected graph formed from a hypercubegraph by adding to it a perfect matching that connects opposite pairs...
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...
bipartite graphs are the crown graphs, formed from complete bipartite graphs by removing the edges of a perfect matching. Hypercubegraphs, partial cubes...
distance graphs include the cactus graphs, the matchstick graphs and penny graphs, and the hypercubegraphs. The generalized Petersen graphs are non-strict...
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 hypercubegraph Q...
step in the graph according to one direction Thus, the walk operator is W = S C {\displaystyle W=SC} . In the case of the hypercubegraph, we can leverage...
product of two hypercubegraphs is another hypercube: Qi□Qj = Qi+j. The Cartesian product of two median graphs is another median graph. The graph of vertices...
other in the hypercubegraph. That is, it is the half-square of the hypercube. This connectivity pattern produces two isomorphic graphs, disconnected...
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...
finite graphs that contains all graphs in F; for instance, every finite tree is a subgraph of a sufficiently large hypercubegraph so a hypercube can be...
dimensions gives the hypercubegraphs (with 2n vertices and degree n). Similarly extension of the octahedron to n dimensions gives the graphs of the cross-polytopes...
equivalent as a metric space to the set of distances between vertices in a hypercubegraph. One can also view a binary string of length n as a vector in R n {\displaystyle...
sometimes called a snake, and the problem of finding long induced paths in hypercubegraphs is known as the snake-in-the-box problem. Similarly, an induced cycle...
within a constant factor. The achromatic number of an n-dimensional hypercubegraph 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 hypercubegraph 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...
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