Edge-fault-tolerant diameter and bipanconnectivity of hypercubes

Chen, Xie-Bin

doi:10.1016/j.ipl.2010.09.012

Cited by 12 publications

(3 citation statements)

References 22 publications

(26 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These parameters were studied by several authors for some Cartesian product graphs [7,25,26] and for the hypercube and its variants [3,5,8,10,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The vulnerability of the diameter of the enhanced hypercubes

West

2017

Theoretical Computer Science

View full text Add to dashboard Cite

For an interconnection network G, the ω-wide diameter d ω (G) is the least ℓ such that any two vertices are joined by ω internally-disjoint paths of length at most ℓ, and the (ω − 1)-fault diameter D ω (G) is the maximum diameter of a subgraph obtained by deleting fewer than ω vertices of G.The enhanced hypercube Q n,k is a variant of the well-known hypercube. Yang, Chang, Pai, and Chan gave an upper bound for d n+1 (Q n,k ) and D n+1 (Q n,k ) and posed the problem of finding the wide diameter and fault diameter of Q n,k . By constructing internally disjoint paths between any two vertices in the enhanced hypercube, for n ≥ 3 and 2 ≤ k ≤ n we prove thatis the diameter of Q n,k . These results mean that interconnection networks modelled by enhanced hypercubes are extremely robust.

show abstract

“…These parameters were studied by several authors for some Cartesian product graphs [7,25,26] and for the hypercube and its variants [3,5,8,10,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

“…They combine connectivity with diameter to measure simultaneously the fault-tolerance and efficiency of parallel processing computer networks. These parameters were studied by several authors for some Cartesian product graphs [7,25,26] and for the hypercube and its variants [3,5,8,10,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

The vulnerability of the diameter of the enhanced hypercubes

West

2017

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…The parameters of some well-known networks such as hypercube, crossed cube etc. were studied in [4,5,9,11,12,15,18].…”

Section: Introductionmentioning

confidence: 99%

Topological properties on the diameters of the integer simplex

2015

Discrete Applied Mathematics

View full text Add to dashboard Cite

show abstract

A Hypercube Variant with Small Diameter

Zhu

2016

J. Graph Theory

View full text Add to dashboard Cite

This article introduces a new variant of hypercubes Hn. The n‐dimensional twisted hypercube Hn is obtained from two copies of the (n−1)‐dimensional twisted hypercube Hn−1 by adding a perfect matching between the vertices of these two copies of Hn−1. We prove that the n‐dimensional twisted hypercube Hn has diameter false(1+o(1)false)n/prefixlog2n. This improves on the previous known variants of hypercube of dimension n and is optimal up to an error of order o(n/prefixlog2n). Another type of hypercube variant Zn,k that has similar structure and properties as Hn is also discussed in the last section.

show abstract

Edge-fault-tolerant diameter and bipanconnectivity of hypercubes

Cited by 12 publications

References 22 publications

The vulnerability of the diameter of the enhanced hypercubes

The vulnerability of the diameter of the enhanced hypercubes

Topological properties on the diameters of the integer simplex

A Hypercube Variant with Small Diameter

Contact Info

Product

Resources

About