Distance-Based Polynomials and Topological Indices for Hierarchical Hypercube Networks

Gao, Tingmei; Ahmed, Iftikhar

doi:10.1155/2021/5877593

Cited by 2 publications

(1 citation statement)

References 39 publications

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“…Network topology is an important factor because it affects the performance of the network. Hypercubes [26] have been recognized as topologies of multiprocessor systems. The class of folded Petersen cubes, proposed by € O hring and Das [27], is constructed by iteratively applying the Cartesian product operation on hypercubes and the Petersen graph [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

The Pessimistic Diagnosability of Folded Petersen Cubes

Kang

et al. 2022

Journal of Mathematics

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Diagnosability is an important metric parameter for measuring the reliability of multiprocessor systems. The pessimistic diagnosis strategy is a classic diagnostic model based on the PMC model. The class of folded Petersen cubes, denoted by FP Q n , k , where n , k ≥ 0 and n , k ≠ 0 , 0 , is introduced as a competitive model of the hypercubes, which is constructed by iteratively applying the Cartesian product operation on the hypercube Q n and the Petersen graph P . In this paper, by exploring the structural properties of the folded Petersen cubes FP Q n , k , we first prove that FP Q n , k is n + 3 k diagnosable under the PMC model. Then, we completely derive that the pessimistic diagnosability of FP Q n , k is 2 n + 6 k − 2 under the PMC model. Furthermore, the diagnosability and the pessimistic diagnosability of the class of folded Petersen cubes, including the hypercube, folded Petersen graph, and hyper Petersen graph, are obtained.

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Section: Introductionmentioning

confidence: 99%

The Pessimistic Diagnosability of Folded Petersen Cubes

Kang

et al. 2022

Journal of Mathematics

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On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks

Kanwal

Shang

Siddiqui

et al. 2021

Mathematical Problems in Engineering

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In this paper, we have taken review of certain topological topological characteristics of subdivision and the line graph of subdivision of Kragujevac tree. A Kragujevac tree is denoted by K , K ∈ Kg q = r 2 t + 1 + 1 , r , with order r 2 t + 1 + 1 and size r 2 t + 1 , respectively. We have computed the Zagreb polynomials, forgotten polynomial, and M-polynomial for Kragujevac tree. Moreover, we have computed topological indices like Zagreb-type indices, reduced reciprocal Randić indices, family of Gourava indices as well as forgotten index. Further, some topological indices that can be directly derived from M-polynomial, i.e., first and second Zagreb index, modified second Zagreb index, Randić and reciprocal Randić index, symmetric division and harmonic index, and inverse sum and augmented Zagreb index are also computed.

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Distance-Based Polynomials and Topological Indices for Hierarchical Hypercube Networks

Cited by 2 publications

References 39 publications

The Pessimistic Diagnosability of Folded Petersen Cubes

The Pessimistic Diagnosability of Folded Petersen Cubes

On Analysis of Topological Aspects for Subdivision of Kragujevac Tree Networks

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