On the bounds of feedback numbers of -star graphs

Wang, Jian; Xü, Xinsheng; Zhu, Dejun; Gao, Liqing; Xu, Jie

doi:10.1016/j.ipl.2012.03.014

Cited by 8 publications

(3 citation statements)

References 4 publications

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“…k−i , respectively, where an (n, k)-star graph has n!/(n − k)! nodes, and θ = min{k − 1, n − k + 1} [9]. Bossard has proposed a method to find an FNS in a hierarchical hypercube [10].…”

Section: Related Workmentioning

confidence: 99%

Feedback Node Sets in Pancake Graphs and Burnt Pancake Graphs

JUNG,

KANEKO

2023

IEICE Trans. Inf. & Syst.

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A feedback node set (FNS) of a graph is a subset of the nodes of the graph whose deletion makes the residual graph acyclic. By finding an FNS in an interconnection network, we can set a check point at each node in it to avoid a livelock configuration. Hence, to find an FNS is a critical issue to enhance the dependability of a parallel computing system. In this paper, we propose a method to find FNS's in n-pancake graphs and n-burnt pancake graphs. By analyzing the types of cycles proposed in our method, we also give the number of the nodes in the FNS in an n-pancake graph, (n−2.875)(n−1)!+1.5(n−3)!, and that in an n-burnt pancake graph, 2 n−1 (n − 1)!(n − 3.5).

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Section: Related Workmentioning

confidence: 99%

Feedback Node Sets in Pancake Graphs and Burnt Pancake Graphs

JUNG,

KANEKO

2023

IEICE Trans. Inf. & Syst.

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“…Focardi et al gave bounds for the decycling number of hypercubes [10]. Many results on the upper bound of the decycling number are proposed, like star graphs [21], (n, k)star graphs [23], bubble sort graphs [24], and so forth [6,11,16,18,19,22,27].…”

Section: Introductionmentioning

confidence: 99%

On the Decycling Number of Bubble-sort Star Graphs

Liu,

Tang,

Chang

2021

Preprint

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Bubble-sort star graphs are a combination of star graphs and bubble sort graphs. They are bipartite graphs and also form a family of Cayley graphs. The decycling number of a graph is the minimum number of vertices whose removal from the graph results in an acyclic subgraph. In this paper, we prove the decycling number D(n) of an n-dimensional bubblesort star graph for n 5. We also show D(n) satisfies the inequalities for n 6:2 − 2( n−1 2 )! + 1 otherwise.

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“…Bounds on the decycling number have been established for some well-known graphs. In particular, Focardi et al [7] gave bounds of decycling number of hypercubes, and Wang et al [10] gave an upper bound of decycling number of star graphs, Wang et al [11] built bounds of decycling number of (n, k)-star graphs and Caragiannis et al [5] established an upper bound of decycling number of meshes.…”

Section: Introductionmentioning

confidence: 99%