Edge-bipancyclicity and edge-fault-tolerant bipancyclicity of bubble-sort graphs

Kikuchi, Yoshihiro; Araki, Tomoyuki

doi:10.1016/j.ipl.2006.05.012

Cited by 40 publications

(3 citation statements)

References 18 publications

(21 reference statements)

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“…The proposition becomes trivial once we note that by hierarchical structure there is a maximal cover of BS n by 6-cycles (b k b k−1 ) 3 and the 6-prism structurally is these two 6-cycles connected together by six edges b i . The illustration is given in Figure 5 Without loss of generality, let us consider the maximal cover of BS 5 by 6-prisms of the canonical form P = P 6 (5,2). The factor graph Γ 5 = BS 5 P 6 = (V, E) is called the graph whose nodes…”

Section: Example Case Of Bsmentioning

confidence: 99%

Small cycles, generalized prisms and Hamiltonian cycles in the Bubble-sort graph

Konstantinova,

Medvedev

2019

Preprint

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The Bubble-sort graph BSn, n 2, is a Cayley graph over the symmetric group Symn generated by transpositions from the set {( 12), (23), . . . , (n − 1n)}. It is a bipartite graph containing all even cycles of length , where 4 n!. We give an explicit combinatorial characterization of all its 4-and 6-cycles. Based on this characterization, we define generalized prisms in BSn, n 5, and present a new approach to construct a Hamiltonian cycle based on these generalized prisms.

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Section: Example Case Of Bsmentioning

confidence: 99%

Small cycles, generalized prisms and Hamiltonian cycles in the Bubble-sort graph

Konstantinova,

Medvedev

2019

Preprint

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“…Y. Suzuki and K. Kaneko [17] gave an O(n 5 )-time algorithm that solves the node-to-set disjoint paths problem in B n . Y. Kikuchi and T. Araki [10] have shown that the bubble sort graph B n is edge-bipancyclic for n ≥ 5, and B n − F is bipancyclic when n ≥ 4 and |F | ≤ n − 3, where F is a subset of E(B n ). T. Araki and Y. Kikuchi [2] showed that the bubble-sort graph B n is hyper-hamiltonian laceable for n ≥ 4, and B n is still hamiltonian laceable and strongly hamiltonian laceable if there are at most n − 3 faulty edges.…”

Section: Lemma 3 [11]mentioning

confidence: 99%

Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model

Zhou

Wang

Xü

et al. 2013

Intelligence Computation and Evolutionary Computation

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As the size of a multiprocessor system increases, processor failure is inevitable, and fault identification in such a system is crucial for reliable computing. The fault diagnosis is the process of identifying faulty processors in a multiprocessor system through testing. For the practical fault diagnosis systems, the probability that all neighboring processors of a processor are faulty simultaneously is very small, and the conditional diagnosability, which is a new metric for evaluating fault tolerance of such systems, assumes that every faulty set does not contain all neighbors of any processor in the systems. This paper shows that the conditional diagnosability of bubble sort graphs B n under the PMC model is 4n − 11 for n ≥ 4, which is about four times its ordinary diagnosability under the PMC model.

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“…The edge-bipancyclicity and the bipancyclicity of different interconnection networks are widely studied. For example, see [10,11,13,14,15,20].…”

Section: Introductionmentioning

confidence: 99%

Edge-Bipancyclicity of Bubble-Sort Star Graphs

Guo

2019

IEEE Access

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The interconnection network considered in this paper is the bubble-sort star graph. The n-dimensional bubble-sort star graph BS n is a bipartite and (2n − 3)-regular graph of order n!. A bipartite graph G is edge-bipancyclic if each edge of G lies on a cycle of all even length l with 4 ≤ l ≤ |V (G)|. In this paper, we show that the n-dimensional bubble-sort star graph BS n is edge-bipancyclic for n ≥ 3 and for each even length l with 4 ≤ l ≤ n!, every edge of BS n lies on at least four different cycles of length l.

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Edge-bipancyclicity and edge-fault-tolerant bipancyclicity of bubble-sort graphs

Cited by 40 publications

References 18 publications

Small cycles, generalized prisms and Hamiltonian cycles in the Bubble-sort graph

Small cycles, generalized prisms and Hamiltonian cycles in the Bubble-sort graph

Conditional Fault Diagnosis of Bubble Sort Graphs under the PMC Model

Edge-Bipancyclicity of Bubble-Sort Star Graphs

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