Edge-fault-tolerant pancyclicity of arrangement graphs

Sun, Sainan; Xu, Min; Wang, Kaishun

doi:10.1016/j.ins.2014.06.046

Cited by 11 publications

(3 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since then a fair amount of work has been done on the arrangement graphs in the literature. For example, the spectra of arrangement graphs were studied in [2,7], the faulty tolerances were investigated in [36,39], and the conditional fault tolerance and the fault diagnosability were given in [40,41]. For more works on the arrangement graphs, we refer the reader to [2,8–12,19,19,23,31,38] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

The symmetry property of (n,k)‐arrangement graph

Yin

Yan

Zhou

et al. 2021

Journal of Graph Theory

View full text Add to dashboard Cite

The ( n , k )‐arrangement graph A ( n , k ) with 1 ≤ k ≤ n − 1, is the graph with vertex set the ordered k‐tuples of distinct elements in { 1 , 2 , … , n } and with two k‐tuples adjacent if they differ in exactly one of their coordinates. The ( n , k )‐arrangement graph was proposed by Day and Tripathi in 1992, and is a widely studied interconnection network topology. The Johnson graph J ( n , k ) with 1 ≤ k ≤ n − 1, is the graph with vertex set the k‐element subsets of { 1 , 2 , … , n }, and with two k‐element subsets adjacent if their intersection has k − 1 elements. In 1989, Brouwer, Cohen and Neumaier determined the automorphism group of J ( n , k ), and in 2015, Dobson and Malnič proved that J ( n , k ) a is Cayley graph if and only if ( n , k ) = ( 8 , 3 ), ( 32 , 3 ) or ( n , 2 ) with n ≡ 3 ( sans-serifmod 4 ) being a prime‐power. In this article we prove that sans-serifAut ( A ( n , k ) ) ≅ S n × S k, and as a byproduct, A ( n , k ) is a normal cover of J ( n , k ). Furthermore, A ( n , k ) is a Cayley graph if and only if ( n , k ) = ( 33 , 4 ), ( 11 , 4 ), ( 9 , 4 ), ( 12 , 5 ), ( 8 , 5 ), ( 9 , 6 ), ( 32 , 29 ), ( 33 , 30 ), ( n , 1 ), ( n , n − 1 ), ( n , n − 2 ), ( q , 2 ) or ( q + 1 , 3 ), where q is a prime‐power. Note that the graph A ( n , n − 1 ) is called the n‐star graph, and its automorphism group can be deduced from a general result given by Feng in 2006. In 1998, Chiang and Chen proved that A ( n , n − 2 ) is a Cayley graph on the alternating group A n, and in 2011, Zhou determined the automorphism group of A ( n , n − 2 ).

show abstract

Section: Introductionmentioning

confidence: 99%

The symmetry property of (n,k)‐arrangement graph

Yin

Yan

Zhou

et al. 2021

Journal of Graph Theory

View full text Add to dashboard Cite

show abstract

“…It is important to consider fault-tolerance in networks since faults may occur in real networks. Two fault models have been studied in many well-known networks, one is the random fault model, which means that faults may occur anywhere without any restriction, see, for example, [13,14,18,24]. The other is the conditional fault model, which assumes that the fault distribution is limited.…”

Section: Introductionmentioning

confidence: 99%

Fault-Free Hamiltonian Cycles in Balanced Hypercubes with Conditional Edge Faults

2019

Int. J. Found. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

The balanced hypercube, BH n , is a variant of hypercube Q n . Zhou et al. [Inform. Sci. 300 (2015) 20-27] proposed an interesting problem that whether there is a fault-free Hamiltonian cycle in BH n with each vertex incident to at least two fault-free edges. In this paper, we consider this problem and show that each fault-free edge lies on a fault-free Hamiltonian cycle in BH n after no more than 4n − 5 faulty edges occur if each vertex is incident with at least two fault-free edges for all n ≥ 2. Our result is optimal with respect to the maximum number of tolerated edge faults.

show abstract

“…The arrangement graph preserves many attractive properties of S n such as the hierarchical structure, vertex and edge symmetry, simple and optimal routing, and many fault tolerance properties [6]. Some basic properties of A n,k such as average distance [5], Hamiltonicity [8], and embedding [7,17] have recently been computed or derived.…”

Section: Introductionmentioning

confidence: 99%

The Super Spanning Connectivity of Arrangement Graphs

2017

Int. J. Found. Comput. Sci.

Self Cite

View full text Add to dashboard Cite

A k-container C(u, v) of a graph G is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k * -container if it is a spanning subgraph of G. A graph G is k *connected if there exists a k * -container between any two different vertices of G. A k-regular graph G is super spanning connected if G is i * -container for all 1 ≤ i ≤ k. In this paper, we prove that the arrangement graph A n,k is super spanning connected if n ≥ 4 and n − k ≥ 2.

show abstract

Edge-fault-tolerant pancyclicity of arrangement graphs

Cited by 11 publications

References 24 publications

The symmetry property of (n,k)‐arrangement graph

The symmetry property of (n,k)‐arrangement graph

Fault-Free Hamiltonian Cycles in Balanced Hypercubes with Conditional Edge Faults

The Super Spanning Connectivity of Arrangement Graphs

Contact Info

Product

Resources

About