Search results
Results from the WOW.Com Content Network
The Hamming graph H(d,q) is, equivalently, the Cartesian product of d complete graphs K q. [1] In some cases, Hamming graphs may be considered more generally as the Cartesian products of complete graphs that may be of varying sizes. [3] Unlike the Hamming graphs H(d,q), the graphs in this more general class are not necessarily distance-regular ...
The graph Q 0 consists of a single vertex, while Q 1 is the complete graph on two vertices. Q 2 is a cycle of length 4. The graph Q 3 is the 1-skeleton of a cube and is a planar graph with eight vertices and twelve edges. The graph Q 4 is the Levi graph of the Möbius configuration. It is also the knight's graph for a toroidal chessboard.
For a fixed length n, the Hamming distance is a metric on the set of the words of length n (also known as a Hamming space), as it fulfills the conditions of non-negativity, symmetry, the Hamming distance of two words is 0 if and only if the two words are identical, and it satisfies the triangle inequality as well: [2] Indeed, if we fix three words a, b and c, then whenever there is a ...
An example of a partial cube with a Hamming labeling on its vertices. This graph is also a median graph.. Every tree is a partial cube. For, suppose that a tree T has m edges, and number these edges (arbitrarily) from 0 to m – 1.
The Hamming scheme, named after Richard Hamming, is also known as the hyper-cubic association scheme, and it is the most important example for coding theory. [1] [2] [3] In this scheme =, the set of binary vectors of length , and two vectors , are -th associates if they are Hamming distance apart.
Examples of applications of the Hamming weight include: In modular exponentiation by squaring , the number of modular multiplications required for an exponent e is log 2 e + weight( e ). This is the reason that the public key value e used in RSA is typically chosen to be a number of low Hamming weight.
In the mathematical field of graph theory, a distance-transitive graph is a graph such that, given any two vertices v and w at any distance i, and any other two vertices x and y at the same distance, there is an automorphism of the graph that carries v to x and w to y. Distance-transitive graphs were first defined in 1971 by Norman L. Biggs and ...
Because the rook's graph for a square chessboard is the Cartesian product of equal-size cliques, it is an example of a Hamming graph. Its dimension as a Hamming graph is two, and every two-dimensional Hamming graph is a rook's graph for a square chessboard. [3] Square rook's graphs are also called "Latin square graphs"; applied to a Latin ...