One-to-one disjoint path covers on alternating group graphs

You, Lihua; Fan, Jianxi; Han, Yuejuan; Jia, Xiaohua

doi:10.1016/j.tcs.2014.09.041

Cited by 19 publications

(6 citation statements)

References 19 publications

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“…Therefore, this component can be used to perform original network operations without degrading most of its capability. For more further investigations on alternating group graphs and split-stars, see also [13], [46], [54].…”

Section: B Literature Related To Alternating Group Graph and Split-starsmentioning

confidence: 99%

Measuring the Vulnerability of Alternating Group Graphs and Split-Star Networks in Terms of Component Connectivity

Hao

Chang

2019

IEEE Access

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For an integer 2, the -component connectivity of a graph G, denoted by κ (G), is the minimum number of vertices whose removal from G results in a disconnected graph with at least components or a graph with fewer than vertices. This is a natural generalization of the classical connectivity of graphs defined in term of the minimum vertex-cut and a good measure of vulnerability for the graph corresponding to a network. So far, the exact values of -connectivity are known only for a few classes of networks and small 's. It has been pointed out in component connectivity of the hypercubes, International Journal of Computer Mathematics 89 (2012) 137-145] that determining -connectivity is still unsolved for most interconnection networks such as alternating group graphs and star graphs. In this paper, by exploring the combinatorial properties and the fault-tolerance of the alternating group graphs AG n and a variation of the star graphs called split-stars S 2 n , we study their -component connectivities. We obtain the following results: 1) κ 3 (AG n ) = 4n − 10 and κ 4 (AG n ) = 6n − 16 for n 4, and κ 5 (AG n ) = 8n − 24 for n 5 and 2) κ 3 (S 2 n ) = 4n − 8, κ 4 (S 2 n ) = 6n − 14, and κ 5 (S 2 n ) = 8n − 20 for n 4.

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Section: B Literature Related To Alternating Group Graph and Split-starsmentioning

confidence: 99%

Measuring the Vulnerability of Alternating Group Graphs and Split-Star Networks in Terms of Component Connectivity

Hao

Chang

2019

IEEE Access

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“…Software testing is another well-known application of multiple disjoint path covers [10]. Node-disjoint path cover or spanning connectivity is an important property to measure the fault tolerance of a network, which has been studied for many networks, such as hypercube-like networks [11], alternating group graphs [12], multi-dimensional toris [13], DCell networks [14], WK-recursive networks [15], generalized Petersen graphs [16], split-star networks [17], and so on.…”

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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“…ere is also research on other graphs. Such as one-to-many disjoint paths of (n, k)-star graph [5] and hyper-star networks [6] and oneto-one disjoint path covers on alternating group graphs [7].…”

Section: Introductionmentioning

confidence: 99%

Vertex-Disjoint Paths in a 3-Ary n-Cube with Faulty Vertices

Wang

2020

Mathematical Problems in Engineering

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The construction of vertex-disjoint paths (disjoint paths) is an important research topic in various kinds of interconnection networks, which can improve the transmission rate and reliability. The k-ary n-cube is a family of popular networks. In this paper, we determine that there are m2≤m≤n disjoint paths in 3-ary n-cube covering Qn3−F from S to T (many-to-many) with F≤2n−2m and from s to T (one-to-many) with F≤2n−m−1 where s is in a fault-free cycle of length three.

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One-to-one disjoint path covers on alternating group graphs

Cited by 19 publications

References 19 publications

Measuring the Vulnerability of Alternating Group Graphs and Split-Star Networks in Terms of Component Connectivity

Measuring the Vulnerability of Alternating Group Graphs and Split-Star Networks in Terms of Component Connectivity

Super Spanning Connectivity of the Folded Divide-and-SwapCube

Vertex-Disjoint Paths in a 3-Ary n-Cube with Faulty Vertices

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