Note on reliability evaluation of arrangement graphs

Li, Xiangjun; Zeng, Xue-Qian; Xu, Jie

doi:10.1016/j.amc.2021.126845

Cited by 3 publications

(2 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Obviously, the higher the (edge-) connectivity is, the more reliable an interconnection network is [2]. As is known, κ(G) ≤ λ(G) ≤ δ(G), where δ(G) is the minimum degree of G. Boesch and Tindell [3] introduced the concepts of super connectivity and super edge-connectivity. A connected graph G is super connected (resp., edge-connected, in short super-κ (resp., super-λ, ) if any minimum vertex-cut (resp., edge-cut) isolates a vertex of G.…”

Section: Introductionmentioning

confidence: 99%

“…The h-restricted (edge)-connectivity and super-κ (resp., super-λ ) graph for some classic interconnection networks have been investigated recently. For instance, Li et al [3] determine that the h-restricted connectivity of the arrangement graph A n,k is n(n − 1)/2 for h is odd and h = n − 3, otherwise the h-restricted connectivity of the arrangement graph A n,k is (h + 2)(n − 2) − h 2 /2 + h for k = 2 and 0 ≤ h ≤ n − 2. Chen et al [6] proved that the hypercube, the twisted cube, the cross cube, the Möbius cube, and the locally twisted cube are super connected and super edge-connected.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Super Vertex (Edge)-Connectivity of Varietal Hypercube

Yin

et al. 2022

Symmetry

View full text Add to dashboard Cite

The reliability measure of networks is of significant importance to the design and maintenance of networks. Based on connectivity, many refined quantitative indicators for the reliability of network systems have been introduced. The super vertex edge-connectivity and cyclic edge-connectivity, as important parameters to evaluate the robustness of networks, are explored extensively. As a variant of the hypercube Qn, the varietal hypercube VQn has better properties than Qn with the same number of edges and vertices. Wang and Xu have proved that VQn is super vertex-connected for n≥1 and is also super edge-connected if n≠2. In this paper, we use another method to prove these results. Moreover, we also obtain the super restricted connectivity and the cyclic edge-connectivity of the varietal hypercube VQn.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%