Complete binary trees in folded and enhanced cubes

Abstract

It is well known that the complete binary tree B n (n ≥ 3) on 2 n ؊ 1 vertices is not embeddable into the n-dimensional hypercube. In this article, we describe a recursive technique to embed B n into the n-dimensional folded and enhanced cubes, if n satisfies certain necessary parity conditions

Conditional edge-fault-tolerant Hamiltonicity of enhanced hypercube

“…The embedding structure, such as linear arrays and rings, are suitable for designing simple algorithms with low communication costs. A large amount of efficient algorithms designed on the two fundamental networks for parallel and distributed computation to solve algebraic problems and graph problems can be found in previous works( [5], [6], [11]). These applications motivate us to study the embedding of Hamiltonian cycle on networks.…”

The Structural Features of Enhanced Hypercube Networks

“…But the enhanced hypercubes are much more attractive than normal hypercubes due to its potential nice topological properties. For instance, in [1], S. A. choudum and R. Usha Nandini showed that a complete binary tree can be embedded in enhanced hypercubes Q n,k under some restricted conditions. Its special case of k = 1 is the wellknown Folded hypercube (denoted by F Q n ) which has received substantial researches ( [7], [12]).…”

“…Recently many variants of Q n have been proposed to improve the performance of Q n , and the most significant ones wielding a lot of influence are generalized hypercube, folded hypercube, twisted hypercube, argument hypercube and enhanced hypercube. ( [1], [6], [7], [12], [5], [4], [3], [9]). …”

Some results on topological properties of folded hypercubes

“…For example, its diameter is n 2 , about half the diameter of Q n [5]; there are n + 1 internally disjoint paths of length at most n 2 + 1 between any pair of vertices [19]; there exists a cycle of every length l with n + 1 l 2 n − 1 if n is even [24]. Many results on folded hypercubes can be found in papers [3,5,6,8,9,11,12,19,[24][25][26].…”