Edge-fault-tolerant edge-bipancyclicity of balanced hypercubes

Abstract

The balanced hypercube, BH n , is a variant of hypercube Q n . Hao et al. [Appl. Math. Comput. 244 (2014) 447-456] showed that there exists a fault-free Hamiltonian path between any two adjacent vertices in BH n with (2n − 2) faulty edges. Cheng et al. [Inform. Sci. 297 (2015) 140-153] proved that BH n is 6-edge-bipancyclic after (2n − 3) faulty edges occur for all n ≥ 2. In this paper, we improve these two results by demonstrating that BH n is 6-edge-bipancyclic even when there exist (2n − 2) faulty edges for all n ≥ 2. Our result is optimal with respect to the maximum number of tolerated edge faults.

Reliability Analysis of Subsystem in Balanced Hypercubes

“…Thus, tasks running on a faulty vertex can be easily converted to its backup vertex [23], which shows a natural fault-tolerance ability of the balanced hypercube that the hypercube does not have. For more properties about the balanced hypercubes, please refer to [25]- [29].…”

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

“…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.…”

“…Thus tasks running on a faulty processor can be shifted to its backup one [21]. With such novel properties above, different aspects of the balanced hypercube were studied extensively, including path and cycle embedding issues [9,13,16,22,23,25], connectivity [15,24], matching preclusion [14], and symmetric properties [26,27].…”

Structure and Substructure Connectivity of Balanced Hypercubes

“…In particular, the balanced hypercube is superior to the hypercube in a sense that it supports an efficient reconfiguration without changing the adjacent relationship among tasks [27]. Some other excellent properties of the balanced hypercube were discussed by many researchers, such as fault-tolerant resource placement problem [11] g-connectivity [18,30,32] and h-connectivity [20], Hamiltonian path (cycle) embedding [5,8,13,29,31], matching preclusion [17] and matching extendability [19], conditional diagnosability [33] and symmetric properties [37,38]. Lin et al [16] Sabir and Meng [25] generalized the results in Q n and studied this problem in the folded hypercube.…”