Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651430 | Discrete Mathematics | 2006 | 7 Pages |
Abstract
The d -dimensional hypercube, HdHd, is the graph on 2d2d vertices, which correspond to the 2d2dd -vectors whose components are either 0 or 1, two of the vertices being adjacent when they differ in just one coordinate. The notion of Hamming graphs (denoted by Kqd) generalizes the notion of hypercubes: The vertices correspond to the qdqdd -vectors where the components are from the set {0,1,2,…,q-1}{0,1,2,…,q-1}, and two of the vertices are adjacent if and only if the corresponding vectors differ in exactly one component. In this paper we show that the pw(Hd)=∑m=0d-1mm2 and the tw(Kqd)=θ(qd/d).
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
L. Sunil Chandran, T. Kavitha,