Connectivity, super connectivity and generalized 3-connectivity of folded divide-and-swap cubes

Zhao, Shu-Li; Chang, Jou–Ming

doi:10.1016/j.ipl.2023.106377

Cited by 4 publications

(3 citation statements)

References 27 publications

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“…The super-connectivity of G (or, respectively, the super edge connectivity), denoted by κ (1) (G) (or λ (1) (G)), is the minimum cardinality of all super vertex cuts (or super edge cuts) in G, if any exist. Many relevant results have been obtained regarding super-connectivity and super edge connectivity [3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Super-Connectivity of the Folded Locally Twisted Cube

2023

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The hypercube Qn is one of the most popular interconnection networks with high symmetry. To reduce the diameter of Qn, many variants of Qn have been proposed, such as the n-dimensional locally twisted cube LTQn. To further optimize the diameter of LTQn, the n-dimensional folded locally twisted cube FLTQn is proposed, which is built based on LTQn by adding 2n−1 complementary edges. Connectivity is an important indicator to measure the fault tolerance and reliability of a network. However, the connectivity has an obvious shortcoming, in that it assumes all the adjacent vertices of a vertex will fail at the same time. Super-connectivity is a more refined index to judge the fault tolerance of a network, which ensures that each vertex has at least one neighbor. In this paper, we show that the super-connectivity κ(1)(FLTQn)=2n for any integer n≥6, which is about twice κ(FLTQn).

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Section: Introductionmentioning

confidence: 99%

Super-Connectivity of the Folded Locally Twisted Cube

2023

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“…FDSC n is constructed based on DSC n by adding one edge to each node of DSC n . Obviously, the connectivity of FDSC n is log 2 n + 2 = d + 2 [23]. In addition, the diameter upper bound of FDSC n is n − 1 and the network cost is O(n log 2 n).…”

Section: Introductionmentioning

confidence: 99%

“…In [24], Chang et al constructed the dual-CIST for FDSC n . In [23], Zhao and Chang investigated the connectivity, super connectivity and generalized 3-connectivity of FDSC n . We can see that DSC n and FDSC n have many better properties than the hypercube.…”

Section: Introductionmentioning

confidence: 99%

Super Spanning Connectivity of the Folded Divide-and-SwapCube

2023

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A k*-container of a graph G is a set of k disjoint paths between any pair of nodes whose union covers all nodes of G. The spanning connectivity of G, κ*(G), is the largest k, such that there exists a j*-container between any pair of nodes of G for all 1≤j≤k. If κ*(G)=κ(G), then G is super spanning connected. Spanning connectivity is an important property to measure the fault tolerance of an interconnection network. The divide-and-swap cube DSCn is a newly proposed hypercube variant, which reduces the network cost from O(n2) to O(nlog2n) compared with the hypercube and other hypercube variants. The folded divide-and-swap cube FDSCn is proposed based on DSCn to reduce the diameter of DSCn. Both DSCn and FDSCn possess many better properties than hypercubes. In this paper, we investigate the super spanning connectivity of FDSCn where n=2d and d≥1. We show that κ*(FDSCn)=κ(FDSCn)=d+2, which means there exists an m-DPC(node-disjoint path cover) between any pair of nodes in FDSCn for all 1≤m≤d+2.

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On Spanning Wide Diameter of Spider Web Networks

Wang,

Sabir

2024

Parallel Process. Lett.

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For any bipartite graph [Formula: see text] with bipartition [Formula: see text] and [Formula: see text], a [Formula: see text]-container [Formula: see text] is a set of [Formula: see text] internally disjoint paths [Formula: see text] between two vertices [Formula: see text] and [Formula: see text] in [Formula: see text], i.e., [Formula: see text]. Moreover, if [Formula: see text] then [Formula: see text] is called a spanning [Formula: see text]-container, denoted by [Formula: see text]. The length of [Formula: see text] is [Formula: see text]. Besides, [Formula: see text] is spanning [Formula: see text]-laceable if there exists a spanning [Formula: see text]-container between any two vertices [Formula: see text] and [Formula: see text] in [Formula: see text]. Assume that [Formula: see text] and [Formula: see text] are two distinct vertices in a spanning [Formula: see text]-laceable graph [Formula: see text]. Let [Formula: see text] be the collection of all [Formula: see text]’s. Define the spanning [Formula: see text]-wide distance between [Formula: see text] and [Formula: see text] in [Formula: see text], [Formula: see text], and the spanning [Formula: see text]-wide diameter of [Formula: see text], [Formula: see text]. In particular, the spanning wide diameter of [Formula: see text] is [Formula: see text], where [Formula: see text] is the connectivity of [Formula: see text]. In the paper we first provide the lower and upper bounds of the wide diameter of a bipartite graph, and then determine the exact values of the spanning wide diameters of the spider web networks [Formula: see text] for [Formula: see text].

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Connectivity, super connectivity and generalized 3-connectivity of folded divide-and-swap cubes

Cited by 4 publications

References 27 publications

Super-Connectivity of the Folded Locally Twisted Cube

Super-Connectivity of the Folded Locally Twisted Cube

Super Spanning Connectivity of the Folded Divide-and-SwapCube

On Spanning Wide Diameter of Spider Web Networks

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