An optimal result on fault-tolerant cycle-embedding in alternating group graphs

Xue, Zhenxia; Liu, Sanyang

doi:10.1016/j.ipl.2009.08.006

Cited by 9 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 1993, Jwo et al [12] first proposed the n-alternating group graph AG n as a topology of interconnection network for multiprocessor systems. The n-alternating group graph AG n possesses sufficient amount of good properties including cycle-embedding [2], [27], [33], and small diameter [12]. Moreover, the alternating group graph is not only pancyclic and hamiltonian-connected [3], but also panconnected [10].…”

Section: Introductionmentioning

confidence: 99%

Minimum Neighborhood of Alternating Group Graphs

2019

View full text Add to dashboard Cite

The minimum neighborhood and combinatorial property are two important indicators of fault tolerance of a multiprocessor system. Given a graph G, θ G (q) is the minimum number of vertices adjacent to a set of q vertices of G (1 ≤ q ≤ |V (G)|). It is meant to determine θ G (q), the minimum neighborhood problem (MNP). In this paper, we obtain θ AG n (q) for an independent set with size q in an n-dimensional alternating group graph AG n , a well-known interconnection network for multiprocessor systems. We first propose some combinatorial properties of AG n. Then, we study the MNP for an independent set of two vertices and obtain that θ AG n (2) = 4n − 10. Next, we prove that θ AG n (3) = 6n − 16. Finally, we propose that θ AG n (4) = 8n − 24. INDEX TERMS Minimum neighborhood, combinatorial property, fault tolerance, independent set, alternating group graphs.

show abstract

Section: Introductionmentioning

confidence: 99%

Minimum Neighborhood of Alternating Group Graphs

2019

View full text Add to dashboard Cite

show abstract

“…For the terminology and notation not given here, we follow [4]. Let F be a set of faulty vertices in an ndimensional alternating group graph AG n .…”

Section: Introductionmentioning

confidence: 99%

“…Let F be a set of faulty vertices in an ndimensional alternating group graph AG n . Theorem 5 in [4] stated that AG n − F is pancyclic if |F | 2n − 6, where n 4. However, there is a flaw in the proof of the theorem.…”

Section: Introductionmentioning

confidence: 99%

“…Let F ⊂ V (AG n ), |F | 2. Then there are a vertex set F ⊂ V (AG n ) and an automorphism π of AG n such that π(F ) = F and |F ∩ V (AG i n )| |F | − 1 for each 1 i n. [4].) Assume n 5 and 2 m n. Let I = {k 1 , k 2 , .…”

Section: Introductionmentioning

confidence: 99%

“…2n − 6, we know f 3 2, f4 1, and f i = 0 for all 5 i n. Thus, there is an l-cycle for each l with 3 l (n − 1)!/2 in AG r n n (i.e. in AG n − F ).…”

mentioning

confidence: 96%

See 2 more Smart Citations