On extra connectivity and extra edge-connectivity of balanced hypercubes

Lü, Huazhong

doi:10.1080/00207160.2016.1148813

Cited by 58 publications

(10 citation statements)

References 41 publications

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“…Yang [13] determined that the 1-extra edge-connectivity of balanced hypercubes BH n is λ 1 (BH n ) = 4n − 2 for n ≥ 2. Lü [6] showed that λ 2 (BH n ) = 6n − 4 for n ≥ 2. Li et al [5] and Yang et al [12] independently proved that λ 3 (BH n ) = 8n − 8 for n ≥ 2.…”

Section: Introductionmentioning

confidence: 99%

The $g$-extra edge-connectivity of balanced hypercubes

Wei

Yang

2020

Preprint

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The g-extra edge-connectivity is an important measure for the reliability of interconnection networks. Recently, Yang et al. [Appl. Math. Comput. 320 (2018) 464-473] determined the 3-extra edge-connectivity of balanced hypercubes BH n and conjectured that the g-extra edge-connectivity of BH n is λ g (BH n ) = 2(g + 1)n − 4g + 4 for 2 ≤ g ≤ 2n − 1. In this paper, we confirm their conjecture for n ≥ 6 − 12 g + 1 and 2 ≤ g ≤ 8, and disprove their conjecture for n ≥ 3e g (BH n ) g + 1 and 9 ≤ g ≤ 2n − 1, where

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Section: Introductionmentioning

confidence: 99%

The $g$-extra edge-connectivity of balanced hypercubes

Wei

Yang

2020

Preprint

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“…Thus tasks running on a faulty processor can be shifted to its backup processor [26]. With such novel properties above, different aspects of the balanced hypercube are studied extensively, including Hamiltonian embedding issues [5,10,15,17,27,29,32], connectivity issues [18,31], matching preclusion and extendability [16,19], and symmetric issues [33,34] and some other topics [11,30]. In this paper, we will consider the problem of paired 2-DPC of the balanced hypercube with faulty edges.…”

Section: Introductionmentioning

confidence: 99%

Paired many-to-many two-disjoint path cover of balanced hypercubes with faulty edges

Lü

2019

J Supercomput

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The balanced hypercube BH n , a variant of the hypercube, was proposed as a desired interconnection network topology. It is known that BH n is bipartite. Assume that S = {s 1 , s 2 , · · · , s 2n−2 } and T = {t 1 , t 2 , · · · , t 2n−2 } are any two sets of vertices in different partite sets of BH n (n ≥ 2). It has been proved that there exists paired 2-disjoint path cover of BH n . In this paper, we prove that there exists unpaired (2n − 2)-disjoint path cover of BH n (n ≥ 2) from S to T , which improved some known results. The upper bound 2n − 2 of the number of disjoint paths in unpaired (2n − 2)-disjoint path cover is best possible.

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“…So both of g-connectivity and h-connectivity are generalizations of the connectivity, which supply more accurate measures to evaluate reliability and faulttolerance of large networks. Moreover, the higher g-connectivity or h-connectivity the network has, the more reliable the network is [6,18]. It is known that there exists no polynomial time algorithm to compute the g-connectivity and h-connectivity of a general graph [2,6].…”

Section: Introductionmentioning

confidence: 99%