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A Note on Two-Generator 2-Group Covers of Cubic symmetric graphs of Order 2p

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Algebra Colloquium 2022年第4期29卷 713-720页

作者： Xue Wang Jinxin Zhou Department of Mathematics Beijing Jiaotong UniversityBeijing 100044China

Let p be a *** this paper,a complete classification of edge-transitive N-covers of a cubic symmetric graph of order 2p is given for the case when N is a twogenerator 2-group whose derived subgroup is either isomorphic to Z_(2)^(3)or generated by at most two *** an application,it is shown that 11 is the smallest value of n for which there exist infinitely many cubic semisymmetric graphs with order of the form 2^(n)p.

关键词： edge-transitive graph symmetric graph bi-Cayley graph N-cover

Heptavalent symmetric graphs of Order 16p

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Algebra Colloquium 2017年第3期24卷 453-466页

作者： Songtao Guo Hailong Hou Yong Xu School of Mathematics and Statistics Henan University of Science and Technology Luoyang Henan 471023 China

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. We classify connected heptavalent symmetric graphs of order 16p for each prime p. As a result, there are two such sporadic graphs with p=3 and 7, and an infinite family of 1-regular normal Cayley graphs on the group Z23 × D2p with 7｜（p - 1）.

关键词： symmetric graph s-transitive graph Cayley graph

Pentavalent symmetric graphs of Order Twice a Prime Square

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Algebra Colloquium 2015年第3期22卷 383-394页

作者： Jiangmin Pan Zhe Liu Xiaofen Yu Department of Mathematics Yunnan University of Finance and Economics Kunming 650221 China College of Science Zhejiang Agriculture and Forestry University Hangzhou 311300 China Department of Mathematics Yunnan University Kunming 650031 China

A classification of pentavalent symmetric graphs of order twice a prime square is given. It is proved that such a graph is a coset graph of Z3.A6 （non-split extension）, or a bi-coset graph of an extra-special group ... 详细信息

关键词： symmetric graph Cayley graph standard double cover automorphism group

Pentavalent symmetric graphs of Order 16p

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Acta Mathematicae Applicatae Sinica 2017年第1期33卷 115-124页

作者： Song-tao GUO Hai-long HOU Jiang-tao SHI School of Mathematics and Statistics Henan University of Science and Technology School of Mathematics and Information Science Yantai University

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.

关键词： symmetric graph s-transitive graph s-regular graph

Automorphisms of Maps with a Given Underlying graph and Their Application to Enumeration

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Acta Mathematica Sinica,English Series 2005年第2期21卷 225-236页

作者： LinFanMAO YanPeiLIU FengTIAN AcademyofMathematicsandSystemsScience ChineseAcademyofSciencesBeijing100080P.R.China InstituteofAppliedMathematics BeijingJiaotongUniversityBeijing100044P.R.China AcademyofMathematicsandSystemsScience ChineseAcademyofScienceBeijing100080P.R.China

A graph is called a semi-regular graph if its automorphism group action onits ordered pair of adjacent vertices is semi-regular. In this paper, a necessary and sufficientcondition for an automorphism of the graph Γ to be an automorphism of a map with the underlyinggraph Γ is obtained. Using this result, all orientation-preserving automorphisms of maps onsurfaces (orientable and non-orientable) or just orientable surfaces with a given underlyingsemi-regular graph Γ are determined. Formulas for the numbers of non-equivalent embeddings of thiskind of graphs on surfaces (orientable, non-orientable or both) are established, and especially, thenon-equivalent embeddings of circulant graphs of a prime order on orientable, non-orientable andgeneral surfaces are enumerated.

关键词： embedding map cayley graph circulant graph symmetric graph automorphismgroup burnside lemma

EQgraphNet:Advancing single-station earthquake magnitude estimation via deep graph networks with residual connections

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Artificial Intelligence in Geosciences 2024年第1期5卷 257-268页

作者： Zhiguo Wang Ziwei Chen Huai Zhang School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an710049ShaanxiPR China School of Information and Communications Engineering Xi’an Jiaotong UniversityXi’an710049ShaanxiPR China College of Earth and Planetary Sciences University of Chinese Academy of Sciences.Beijing100049BeijingPR China

Magnitude estimation is a critical task in seismology,and conventional methods usually require dense seismic station arrays to provide data with sufficient spatiotemporal *** this context,we propose the Earthquake graph Network(EQgraphNet)to enhance the performance of single-station magnitude *** backbone of the proposed model consists of eleven convolutional neural network layers and ten RCGL modules,where a RCGL combines a Residual Connection and a graph convolutional Layer capable of mitigating the over-smoothing problem and simultaneously extracting temporal features of seismic *** work uses the STanford EArthquake Dataset for model training and performance *** with three existing deep learning models,EQgraphNet demonstrates improved accuracy for both local magnitude and duration magnitude *** evaluate the robustness,we add natural background noise to the model input and find that EQgraphNet achieves the best results,particularly for signals with lower signal-to-noise ***,by replacing various network components and comparing their estimation performances,we illustrate the contribution of each part of EQgraphNet,validating the rationality of our *** also demonstrate the generalization capability of our model across different earthquakes occurring environments,achieving mean errors of±0.1 ***,by demonstrating the effectiveness of deeper architectures,this work encourages further exploration of deeper GNN models for both multi-station and single-station magnitude estimation.

关键词： Magnitude estimation graph neural network symmetric graph Single-station seismic signals

Normality of Tetravalent Cayley graphs of Odd Prime-cube Order and Its Application

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Acta Mathematica Sinica,English Series 2005年第4期21卷 903-912页

作者： Yan Quan FENG Ming Yao XU Department of Mathematics Beijing Jiaotong University Beijing 100044 P. R. China LMAM Institute of Mathematics Peking University Beijing 100871 P. R. China

Let p be an odd prime. In this paper we prove that all tetravalent connected Cayley graphs of order p^3 are normal. As an application, a classification of tetravalent symmetric graphs of odd prime-cube order is given.

关键词： Cayley graph Normal Cayley graph symmetric graph

（G, s）-Transitive graphs of Valency 7

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Algebra Colloquium 2016年第3期23卷 493-500页

作者： Songtao Guo Yantao Li Xiaohui Hua School of Mathematics and Statistics Henan University of Science and Technology Luoyang Henan 471023 China College of Arts and Science Beijing Union University Beijing 100091 China College of Mathematics and Information Science Henan Normal University Xinxiang Henan 453007 China

Let X be a finite simple undirected graph and G an automorphism group of X. If G is transitive on s-arcs but not on （s ＋ 1）-arcs then X is called （G, s）-transitive. Let X be a connected （G, s）-transitive graph of a prime valency p, and Gv the vertex stabilizer of a vertex v E V（X） in G. For the case p = 3, the exact structure of Gv has been determined by Djokovid and Miller in [Regular groups of automorphisms of cubic graphs, J. Combin. Theory （Ser. B） 29 （1980） 195-230]. For the case p = 5, all the possibilities of Gv have been given by Guo and Feng in [A note on pentavalent s-transitive graphs, Discrete Math. 312 （2012） 2214-2216]. In this paper, we deal with the case p = 7 and determine the exact structure of the vertex stabilizer Gv.

关键词： symmetric graph s-transitive graph (G s)-transitive graph

On symmetric Cayley graphs of Valency Eleven

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Algebra Colloquium 2021年第2期28卷 309-318页

作者： Bo Ling Bengong Lou Li Ma Xue Yu School of Mathematics and Computer Sciences Yunnan Minzu University Kunming 650504China School of Mathematics and Statistics Yunnan University Kunming 650031China College of Mathematics and Statistics Qujing Normal University QujingYunnan 655011China Department of Mathematics Henan Institute of Science and Technology XinxiangHenan 453003China

A Cayley graph Г=Cay(G,S)is said to be normal if G is normal in Aut Г.In this paper,we investigate the normality problem of the connected 11-valent symmetric Cayley graphs Г of finite nonabelian simple groups G,where the vertex stabilizer A_(u) is soluble for A=Aut Г and v∈∨Г.We prove that either Г is normal or G=A_(5),A_(10),A_(54),A_(274),A_(549) or A_(1099).Further,11-valent symmetric nonnormal Cayley graphs of As,A54 and A274 are *** provides some more examples of nonnormal 11-valent symmetric Cayley graphs of finite nonabelian simple groups after the first graph of this kind(of valency 11)was constructed by Fang,Ma and Wang in 2011.

关键词： nonabelian simple group normal Cayley graph symmetric graph