Fault diameter of Cartesian product graphs

Xu, Min; Xu, Jie; Hou, Xinmin

doi:10.1016/j.ipl.2004.11.005

Cited by 45 publications

(26 citation statements)

References 10 publications

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“…We consider the fault diameter of Cartesian graph bundles, a class of graphs that includes Cartesian product graphs. In the case when the bundle is a product, our theorem reduces to the result given in [12].…”

Section: Introductionmentioning

confidence: 91%

“…Since nodes of a network do not always work, if some nodes are faulty, some information may not be transmitted by some of these nodes. The fault diameter has been determined for many important networks recently [3,4,8,12]. The concept of fault diameter of Cartesian product graphs was first described in [7], but the upper bound was wrong, as shown by Xu et al [12] who corrected the mistake.…”

Section: Introductionmentioning

confidence: 99%

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Fault-diameter of Cartesian graph bundles

Banič

Žerovnik

2006

Information Processing Letters

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Section: Introductionmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Fault-diameter of Cartesian graph bundles

Banič

Žerovnik

2006

Information Processing Letters

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“…A lot of work has been done on various aspects of network fault tolerance, see for example the survey [6] and more recent papers [9,13,15]. In particular the fault diameter with faulty vertices which was first studied in [11] and the edge fault diameter has been determined for many important networks recently [8,7,12,14]. In most papers either only edge faults or only vertex faults are considered, while the case when both edges and vertices may be faulty is studied rarely.…”

Section: Introductionmentioning

confidence: 99%

Edge, vertex and mixed fault diameters

Banič

Erveš

Žerovnik

2009

Advances in Applied Mathematics

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Let ▫${mathcal{D}}^E_q(G)$▫ denote the maximum diameter among all subgraphs obtained by deleting ▫$q$▫ edges of ▫$G$▫. Let ▫${mathcal{D}}^V_p(G)$▫ denote the maximum diameter among all subgraphs obtained by deleting ▫$p$▫ vertices of ▫$G$▫. We prove that ▫${mathcal{D}}^E_a(G) leqslant {mathcal{D}}^V_a(G) + 1$▫ a for all meaningful ▫$a$▫. We also define mixed fault diameter ▫${mathcal{D}}^M_{(p,q)}(G)$▫, where ▫$p$▫ vertices and ▫$q$▫ edges are deleted at the same time. We prove that for ▫$0 < l leqslant a$▫, ▫${mathcal{D}}^E_a(G) leqslant {mathcal{D}}^M_{(a-ell,ell)}(G) leqslant {mathcal{D}}^V_a(G) + 1$▫, and give some examples

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“…These parameters were studied by several authors for some Cartesian product graphs [7,25,26] and for the hypercube and its variants [3,5,8,10,18,19,20].…”

Section: Introductionmentioning

confidence: 99%

The vulnerability of the diameter of the enhanced hypercubes

West

2017

Theoretical Computer Science

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For an interconnection network G, the ω-wide diameter d ω (G) is the least ℓ such that any two vertices are joined by ω internally-disjoint paths of length at most ℓ, and the (ω − 1)-fault diameter D ω (G) is the maximum diameter of a subgraph obtained by deleting fewer than ω vertices of G.The enhanced hypercube Q n,k is a variant of the well-known hypercube. Yang, Chang, Pai, and Chan gave an upper bound for d n+1 (Q n,k ) and D n+1 (Q n,k ) and posed the problem of finding the wide diameter and fault diameter of Q n,k . By constructing internally disjoint paths between any two vertices in the enhanced hypercube, for n ≥ 3 and 2 ≤ k ≤ n we prove thatis the diameter of Q n,k . These results mean that interconnection networks modelled by enhanced hypercubes are extremely robust.

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Fault diameter of Cartesian product graphs

Cited by 45 publications

References 10 publications

Fault-diameter of Cartesian graph bundles

Fault-diameter of Cartesian graph bundles

Edge, vertex and mixed fault diameters

The vulnerability of the diameter of the enhanced hypercubes

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