Embedding hypercubes, rings, and odd graphs into hyper-stars

Kim, Jong-Seok; Cheng, Eddie; Lipták, László; Lee, Hyeong-Ok

doi:10.1080/00207160701691431

Cited by 21 publications

(10 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For examples, it has better scalability, simple routing algorithm, maximum fault‐tolerance and lower network cost (defined as the product of its degree and diameter) than the hypercube and its variations . Many properties of hyper‐star and folded hyper‐star graphs were introduced in . Please note that there is a similarly named network called hyperstar , which is completely different from the hyper‐star studied in this paper.…”

Section: Introductionmentioning

confidence: 99%

Hyper‐star graphs: Some topological properties and an optimal neighbourhood broadcasting algorithm

Zhang

Qiu

Kim

2015

Concurrency and Computation

View full text Add to dashboard Cite

Summary Hyper‐star graph HS(2n,n) was introduced to be a competitive model to both hypercubes and star graphs. In this paper, we study its properties by (1) giving a closed form solution to the surface area of HS(2n,n), (2) discussing its Hamiltonicity by establishing an isomorphism between the graph and the well‐known middle levels problem, and (3) showing that full binary trees can be embedded into HS(2n,n) with dilation 1. We also develop a single‐port optimal neighbourhood broadcasting algorithm for HS(2n,n). Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

Section: Introductionmentioning

confidence: 99%

Hyper‐star graphs: Some topological properties and an optimal neighbourhood broadcasting algorithm

Zhang

Qiu

Kim

2015

Concurrency and Computation

View full text Add to dashboard Cite

show abstract

“…The former is the odd graph O k+1 , where, for any integer k ≥ 2, the vertex-set corresponds to the set of all possible k-element subsets of a (2k + 1)-element set, and two vertices are adjacent if and only if the corresponding k-subsets are disjoint. The latter is sometimes referred to as the revolving door graph, the middle-levels graph [11], the middle cube M Q 2k+1 = Q 2k+1 (k, k + 1) [10], or the regular hyperstar graph HS(2(k + 1), k + 1) [16,20,21].…”

Section: Introductionmentioning

confidence: 99%

The super-connectivity of odd graphs and of their kronecker double cover

Ek̇inċi

Gauci

2021

RAIRO-Oper. Res.

View full text Add to dashboard Cite

The study of connectivity parameters forms an integral part of the research conducted in establishing the fault tolerance of networks. A number of variations on the classical notion of connectivity have been proposed and studied. In particular, the super--connectivity asks for the minimum number of vertices that need to be deleted from a graph in order to disconnect the graph without creating isolated vertices. In this work, we determine this value for two closely related families of graphs which are considered as good models for networks, namely the odd graphs and their Kronecker double cover. The odd graphs are constructed by taking all possible subsets of size $k$ from the set of integers $\{1,\ldots,2k+1\}$ as vertices, and defining two vertices to be adjacent if the corresponding $k$-subsets are disjoint; these correspond to the Kneser graphs $KG(2k+1,k)$. The Kronecker double cover of a graph $G$ is formed by taking the Kronecker product of $G$ with the complete graph on two vertices; in the case when $G$ is $KG(2k+1,k)$, the Kronecker double cover is the bipartite Kneser graph $H(2k+1,k)$. We show that in both instances, the super--connectivity is equal to $2k$.

show abstract

“…They further proposed an efficient broadcasting scheme for HS(2k, k) based on a spanning tree with minimum height. Stronger structural properties (such as edge-symmetry, super-connectivity, and orientability) and some embedding schemes for hyper-stars were provided in [3,4] and [17], respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Properties of hyper-stars and folded hyper-stars were discussed in [3,4,17,18] and [19], respectively. Lee et al [19] showed that HS(n, k) is isomorphic to HS(n, n − k) and has diameter n − 1, and FHS(2k, k) has diameter k. Moreover, a result in [19] also showed that hyper-stars and folded hyperstars have a lower network cost (measured by the product of degree and diameter) than that of hypercubes, folded hypercubes, and other variants with the same number of nodes.…”

Section: Introductionmentioning

confidence: 99%

Independent spanning trees on folded hyper‐stars

Yang

Chang

2010

Networks

View full text Add to dashboard Cite

Fault-tolerant broadcasting and secure message distribution are important issues for numerous applications in networks. It is a common idea to design multiple independent spanning trees (ISTs) as a broadcasting scheme or a distribution protocol for receiving high levels of fault-tolerance and security. Recently, hyper-stars were introduced as a competitive model of interconnection network for both hypercubes and star graphs. The class of folded hyper-stars is a strengthened variation of hyper-stars obtained by adding additional links to connect complemented nodes. Both hyper-stars and folded hyper-stars have been shown to have lower network cost (measured by the product of degree and diameter) than hypercubes, folded hypercubes, and other variants. In this article, we propose an algorithm to construct k + 1 ISTs on a regular folded hyper-star FHS(2k , k ), where the number of ISTs matches the connectivity of FHS(2k , k ). In particular, for k ≥ 4, the constructed k ISTs have height 2k − 2, and the other one has height k + 1.

show abstract

Embedding hypercubes, rings, and odd graphs into hyper-stars

Cited by 21 publications

References 8 publications

Hyper‐star graphs: Some topological properties and an optimal neighbourhood broadcasting algorithm

Hyper‐star graphs: Some topological properties and an optimal neighbourhood broadcasting algorithm

The super-connectivity of odd graphs and of their kronecker double cover

Independent spanning trees on folded hyper‐stars

Contact Info

Product

Resources

About