Search results
Results from the WOW.Com Content Network
In graph theory, the hypercube graph Q n is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q 3 is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. Q n has 2 n vertices, 2 n – 1 n edges, and is a regular graph with n edges touching each vertex.
This can be generalized to any number of dimensions. This process of sweeping out volumes can be formalized mathematically as a Minkowski sum: the d-dimensional hypercube is the Minkowski sum of d mutually perpendicular unit-length line segments, and is therefore an example of a zonotope. The 1-skeleton of a hypercube is a hypercube graph.
The resulting graph is a bipartite Kneser graph; the graph formed in this way with n = 2 has 20 vertices and 30 edges, and is called the Desargues graph. All median graphs are partial cubes. [3] The trees and hypercube graphs are examples of median graphs. Since the median graphs include the squaregraphs, simplex graphs, and Fibonacci cubes, as ...
Let n be a positive integer, and let γ be a real number in the unit interval 0 ≤ γ ≤ 1.Suppose additionally that (1 − γ)n is an even number.Then the Frankl–Rödl graph is the graph on the 2 n vertices of an n-dimensional unit hypercube [0,1] n in which two vertices are adjacent when their Hamming distance (the number of coordinates in which the two differ) is exactly (1 − γ)n. [2]
This is an example of how to apply the quantum walk search on a hypercube graph. [12] Four-dimensional hypercube with binary labels. Although in the original description Szegedy quantum walks are used, for this example we show the use of coined quantum walk as it is more intuitive to understand.
The middle layer graph of an odd-dimensional hypercube graph Q 2n+1 (n,n+1) is a subgraph whose vertex set consists of all binary strings of length 2n + 1 that have exactly n or n + 1 entries equal to 1, with an edge between any two vertices for which the corresponding binary strings differ in exactly one bit. Every middle layer graph is ...
For example, with a x3 multiplier, each match made with a full speed bonus would be worth 3750 points. ... try creating and using a Hypercube or Star Gem. 5. When you earn a Hypercube, don't waste ...
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, respectively) have distinguishing number three. However, every hypercube graph of higher dimension has distinguishing number only two. [4] The Petersen graph has distinguishing number 3.