Decycling bubble sort graphs

Wang, Jian; Xü, Xinsheng; Gao, Liqing; Zhang, Sijia; Yang, Yuansheng

doi:10.1016/j.dam.2015.05.024

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…(2n − 3)/4(n − 1), respectively, where an n-bubble sort graph has n! nodes [12]. Xu et al have shown that the lower and upper bounds of the number of nodes of an MFNS in a crossed cube are 2 n−1 (n − 2)/(n − 1) and 2 n−1 , respectively [13].…”

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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“…Improving the bound on the decycling number of hypercubes was continued in [2] and [13]. This body of work inspired research on the decycling number of other practical network structures [20,21]. In more traditional graph theoretic directions, there has been progress on bounding the decycling of regular graph in general [14], as well as for cubic graphs specifically [15,16] including finding the exact decycling number of the (generalized) Petersen graph [8].…”

Section: Introductionmentioning

confidence: 99%

Cycle intersection graphs and minimum decycling sets of even graphs

Cary

2020

Discrete Math. Algorithm. Appl.

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We introduce the cycle intersection graph of a graph, an adaptation of the cycle graph of a graph, and use the structure of these graphs to prove an upper bound for the decycling number of all even graphs. This bound is shown to be significantly better when an even graph admits a cycle decomposition in which any two cycles intersect in at most one vertex. Links between the cycle rank of the cycle intersection graph of an even graph and the decycling number of the even graph itself are found. The problem of choosing an ideal cycle decomposition is addressed and is presented as an optimization problem over the space of cycle decompositions of even graphs.

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Decycling bubble sort graphs

Abstract: a b s t r a c tThe decycling number of a graph G is the minimum number of vertices whose removal from G results in an acyclic subgraph. In this paper we show that the decycling number f (n) of the bubble sort graph B n satisfies these inequalities:.

Cited by 3 publications

References 7 publications

Feedback Node Sets in Pancake Graphs and Burnt Pancake Graphs

Feedback Node Sets in Pancake Graphs and Burnt Pancake Graphs

On the Decycling Number of Bubble-sort Star Graphs

Cycle intersection graphs and minimum decycling sets of even graphs

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