<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>h</mml:mi></mml:math>-restricted connectivity of locally twisted cubes

Wei, Chia-Chen; Hsieh, Sun Yuan

doi:10.1016/j.dam.2016.08.012

Cited by 44 publications

(6 citation statements)

References 37 publications

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“…Work related to the R g -connectivity for special networks and small values of g can be found in the literature see, for example, [3,9,11,19,22,27] . The following lemmas are very useful for proving our main results.…”

Section: Definition 25 [6]mentioning

confidence: 99%

“…Lemma 2.13[7] For any positive integer n, there is no cycle of length 3 in the locally twisted cube LT Q n . Lemma 2.14[19] Let H be a subgraph of LT Q n . If δ(H) = g, then |V (H)| ≥ 2 g , where 0 ≤ g ≤ n and n ≥ 2.Lemma 2.15[19] For an n-dimensional locally twisted cube LT Q n…”

mentioning

confidence: 99%

“…Lemma 2.14[19] Let H be a subgraph of LT Q n . If δ(H) = g, then |V (H)| ≥ 2 g , where 0 ≤ g ≤ n and n ≥ 2.Lemma 2.15[19] For an n-dimensional locally twisted cube LT Q n…”

mentioning

confidence: 99%

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The g-Good-Neighbor Conditional Diagnosability of Locally Twisted Cubes

Wei

2017

J. Oper. Res. Soc. China

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Section: Definition 25 [6]mentioning

confidence: 99%

mentioning

confidence: 99%

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The g-Good-Neighbor Conditional Diagnosability of Locally Twisted Cubes

Wei

2017

J. Oper. Res. Soc. China

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“…Ye and Liang [16] established that κ h is also 2 h (n−h) for some members of hypercube-like networks such as Crossed cubes, Locally twisted cubes, Möbius cubes. Independently, Wei and Hsieh [14] determined κ h for the Locally twisted cubes. Ning [13] obtained κ h for the exchanged crossed cubes.…”

Section: Introductionmentioning

confidence: 99%

On conditional connectivity of the Cartesian product of cycles

Borse¹,

Mundhe²,

Saraf³

2020

Discuss. Math. Graph Theory

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The conditional h-vertex (h-edge) connectivity of a connected graph H of minimum degree k > h is the size of a smallest vertex (edge) set F of H such that H − F is a disconnected graph of minimum degree at least h. Let G be the Cartesian product of r ≥ 1 cycles, each of length at least four and let h be an integer such that 0 ≤ h ≤ 2r − 2. In this paper, we determine the conditional h-vertex-connectivity and the conditional hedge -connectivity of the graph G. We prove that both these connectivities are equal to (2r −h)a r h , where a r h is the number of vertices of a smallest h-regular subgraph of G.

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“…Ye and Liang [16] obtained a lower bound on the conditional h-vertex connectivity κ h of the graph G n and established that κ h is 2 h (n−h) for some members of hypercubelike networks such as Crossed cubes, Locally twisted cubes, Möbius cubes. Independently, Wei and Hsieh [14] determined κ h for the Locally twisted cubes. Ning [13] obtained κ h for the exchanged crossed cubes.…”

Section: Introductionmentioning

confidence: 99%

On conditional connectivity of the Cartesian product of cycles

Saraf¹,

Borse²,

Mundhe³

2020

Preprint

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The conditional h-vertex(h-edge) connectivity of a connected graph H of minimum degree k > h is the size of a smallest vertex(edge) set F of H such that H − F is a disconnected graph of minimum degree at least h. Let G be the Cartesian product of r ≥ 1 cycles, each of length at least four and let h be an integer such that 0 ≤ h ≤ 2r − 2. In this paper, we determine the conditional h-vertex-connectivity and the conditional h-edge-connectivity of the graph G. We prove that both these connectivities are equal to (2r − h)a r h , where a r h is the number of vertices of a smallest h-regular subgraph of G.

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h-restricted connectivity of locally twisted cubes

Cited by 44 publications

References 37 publications

The g-Good-Neighbor Conditional Diagnosability of Locally Twisted Cubes

The g-Good-Neighbor Conditional Diagnosability of Locally Twisted Cubes

On conditional connectivity of the Cartesian product of cycles

On conditional connectivity of the Cartesian product of cycles

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