On Conditional
            <i>h</i>
            ‐Vertex Connectivity of Some Networks

Ye, Liang-Cheng; Liang, Jiarong

doi:10.1049/cje.2016.05.023

Cited by 21 publications

(5 citation statements)

References 21 publications

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“…Li and Xu [10] proved that λ h of any n-dimensional hypercube-like network G n is also 2 h (n − h). 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.…”

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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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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show abstract

“…Li and Xu [10] proved that λ h of any n-dimensional hypercube-like network G n is also 2 h (n − h). 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.…”

Section: Introductionmentioning

confidence: 99%

On conditional connectivity of the Cartesian product of cycles

Saraf¹,

Borse²,

Mundhe³

2020

Preprint

View full text Add to dashboard Cite

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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“…To address the shortcomings of the connectivity stated above, Harary [9] introduced the conditional connectivity of a connected graph by adding some constraints on the components of the resulting graph after vertex deletion. After that, several kinds of conditional connectivity were proposed and investigated [4,6,7,10,23,26,35], such as g-connectivity and h-connectivity.…”

Section: Introductionmentioning

confidence: 99%

“…It is known that there exists no polynomial time algorithm to compute the g-connectivity and h-connectivity of a general graph [2,6]. The h-connectivity [4,14,23,24,26,35] and g-connectivity [3,10,15,28,34,36] of some famous networks are investigated in the literature.…”

Section: Introductionmentioning

confidence: 99%