Combinatorial properties of the generalized n-cubes - Tripathi, Pramila (2002)
We define a generalized n-cube Q(n,k) as a graph whose vertices are the binary n-tuples denoted by a1a2...an such that two vertices are adjacent whenever they differ in exactly k coordinates. In this paper, we will show isomorphism between Q(n,k) and Q(n,n-k) for n even and k odd. This extends the results of Galliguez and Alipan. We also define a graph S(n,k) and show that the diameter of S(n,k) and Q(n,k) is at most r+1 when n=rk + 1. Otherwise the diameter of S(n,k) and Q(n,k) is at most [n over k + 1] for k <_ [n over 2].
Thesis (M.S. Computer Science)--University of the Philippines, Diliman.
Keywords: Hypercube networks (Computer networks).; Computer networks