On Reconstruction of Normal Edge-Transitive Cayley Graphs

Khosravi, Behrooz; Khosravi, Bahman

doi:10.1007/s00026-020-00514-3

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…According to the randomness of the business data of the Internet of ings and renewable energy, the interval time of continuous time scale division is set as Δt. e decision moment and decision cycle Δt can be dynamically adjusted by using the above cycle to meet the complexity and variability of the edge algorithm of the Internet of ings [14]. At each calculation decision moment point, the generation rate and output rate of business data are set as W and E, respectively; then, the accumulated data volume and energy value of the Internet of ings in the calculation cycle of constant time interval can be expressed in the following formulas:…”

Section: Cycle Setting Of Iot Edge Algorithmmentioning

confidence: 99%

Research on Evaluation Method of Sports Events Based on Edge Algorithm

Deng

Gudamu

2021

Security and Communication Networks

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In view of the high computational cost and long computational time of IoT edge algorithm in traditional sports event evaluation, this paper optimizes IoT edge algorithm by introducing deep reinforcement learning technology. Set the IoT edge algorithm cycle through the IoT topology to obtain the data upload speed. In order to improve the evaluation efficiency of sports events, the process of edge algorithm is designed. The contribution rate of evaluation index is calculated, and the consistency, minimum deviation, and minimum difference of the results are taken as the standard to design the evaluation method of sports events. In order to verify the performance of the optimized edge algorithm, the test data set and test platform are set up and the comparative experiment is designed. Compared with the traditional methods, the edge algorithm based on DSLL has lower computational cost, shorter computational time, higher evaluation accuracy, and more practical results.

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Section: Cycle Setting Of Iot Edge Algorithmmentioning

confidence: 99%

Research on Evaluation Method of Sports Events Based on Edge Algorithm

Deng

Gudamu

2021

Security and Communication Networks

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“…Our main result relies on certain graph constructions which we define in Subsection 3.1, namely the direct product n i=1 Γ i of a family of graphs Γ i , and a full subdirect product of a graph direct product. A different graph theoretical construction was used recently in [8] to study normal edge-transitive Cayley graphs Cay(G; C) of groups G admitting a direct decomposition G = M × N with both M, N ∈ A(G; C), but the analysis in [8] does not apply in our general situation.…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

Normal edge-transitive Cayley graphs and Frattini-like subgroups

Khosravi¹,

Praeger²

2021

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For a finite group G and an inverse-closed generating set C of G, let Aut(G; C) consist of those automorphisms of G which leave C invariant. We define an Aut(G; C)-invariant normal subgroup Φ(G; C) of G which has the property that, for any Aut(G; C)-invariant normal set of generators for G, if we remove from it all the elements of Φ(G; C), then the remaining set is still an Aut(G; C)invariant normal generating set for G. The subgroup Φ(G; C) contains the Frattini subgroup Φ(G) but the inclusion may be proper. The Cayley graph Cay(G, C) is normal edge-transitive if Aut(G; C) acts transitively on the pairs {c, c −1 } from C. We show that, for a normal edge-transitive Cayley graph Cay(G, C), its quotient modulo Φ(G; C) is the unique largest normal quotient which is isomorphic to a subdirect product of normal edge-transitive graphs of characteristically simple groups. In particular, we may therefore view normal edge-transitive Cayley graphs of characteristically simple groups as building blocks for normal edge-transitive Cayley graphs whenever we have Φ(G; C) trivial. We explore several questions which these results raise, some concerned with the set of all inverse-closed generating sets for groups in a given family. In particular we use this theory to classify all 4-valent normal edge-transitive Cayley graphs for dihedral groups; this involves a new construction of an infinite family of examples, and disproves a conjecture of Talebi.

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Normal edge-transitive Cayley graphs and Frattini-like subgroups

Khosravi

Praeger

2022

Journal of Algebra

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On Reconstruction of Normal Edge-Transitive Cayley Graphs

Cited by 3 publications

References 25 publications

Research on Evaluation Method of Sports Events Based on Edge Algorithm

Research on Evaluation Method of Sports Events Based on Edge Algorithm

Normal edge-transitive Cayley graphs and Frattini-like subgroups

Normal edge-transitive Cayley graphs and Frattini-like subgroups

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