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Pentavalent Symmetric Graphs of Order Twice a Prime Square 被引量:2
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作者 Jiangmin Pan Zhe Liu Xiaofen Yu 《Algebra Colloquium》 SCIE CSCD 2015年第3期383-394,共12页
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 ... 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 of order 125, or the standard double cover of a specific abelian Cayley digraph of order a prime square. 展开更多
关键词 symmetric graph Cayley graph standard double cover automorphism group
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Pentavalent Symmetric Graphs of Order 16p 被引量:1
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作者 Song-tao GUO Hai-long HOU Jiang-tao SHI 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第1期115-124,共10页
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 fo... 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. 展开更多
关键词 symmetric graph s-transitive graph s-regular graph
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Pentavalent symmetric graphs of order 2p^3 被引量:1
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作者 YANG DaWei Feng YanQuan 《Science China Mathematics》 SCIE CSCD 2016年第9期1851-1868,共18页
A graph is symmetric or 1-regular if its automorphism group is transitive or regular on the arc set of the graph, respectively. We classify the connected pentavalent symmetric graphs of order 2p^3 for each prime p. Al... A graph is symmetric or 1-regular if its automorphism group is transitive or regular on the arc set of the graph, respectively. We classify the connected pentavalent symmetric graphs of order 2p^3 for each prime p. All those symmetric graphs appear as normal Cayley graphs on some groups of order 2p^3 and their automorphism groups are determined. For p = 3, no connected pentavalent symmetric graphs of order 2p^3 exist. However, for p = 2 or 5, such symmetric graph exists uniquely in each case. For p 7, the connected pentavalent symmetric graphs of order 2p^3 are all regular covers of the dipole Dip5 with covering transposition groups of order p^3, and they consist of seven infinite families; six of them are 1-regular and exist if and only if 5 |(p- 1), while the other one is 1-transitive but not 1-regular and exists if and only if 5 |(p ± 1). In the seven infinite families, each graph is unique for a given order. 展开更多
关键词 Cayley graph symmetric graph regular cover
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A Note on Two-Generator 2-Group Covers of Cubic Symmetric Graphs of Order 2p
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作者 Xue Wang Jinxin Zhou 《Algebra Colloquium》 SCIE CSCD 2022年第4期713-720,共8页
Let p be a prime.In 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 isomo... Let p be a prime.In 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 elements.As 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. 展开更多
关键词 edge-transitive graph symmetric graph bi-Cayley graph N-cover
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Heptavalent Symmetric Graphs with Certain Conditions
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作者 Jiali Du Yanquan Feng +1 位作者 Yuqin Liu Genghua Fan 《Algebra Colloquium》 SCIE CSCD 2021年第2期243-252,共10页
A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vert... A graph Γ is said to be symmetric if its automorphism group Aut(Γ)acts transitively on the arc set of Γ.We show that if Γ is a finite connected heptavalent symmetric graph with solvable stabilizer admitting a vertex-transitive non-abelian simple group G of automorphisms,then either G is normal in Aut(Γ),or Aut(Γ)contains a non-abelian simple normal subgroup T such that G≤T and(G,T)is explicitly given as one of 11 possible exceptional pairs of non-abelian simple groups.If G is arc-transitive,then G is always normal in Aut(Γ),and if G is regular on the vertices of Γ,then the number of possible exceptional pairs(G,T)is reduced to 5. 展开更多
关键词 symmetric graph Cayley graph coset graph simple group
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Heptavalent Symmetric Graphs of Order 16p
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作者 Songtao Guo Hailong Hou Yong Xu 《Algebra Colloquium》 SCIE CSCD 2017年第3期453-466,共14页
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 spora... 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). 展开更多
关键词 symmetric graph s-transitive graph Cayley graph
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Normal edge-transitive Cayley graphs on a class of non-abelian groups
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作者 Nuo LI Qi DENG Hua ZHANG 《Frontiers of Mathematics in China》 CSCD 2024年第4期215-227,共13页
Let Г=Cay(G,S)be the Cayley graph of a group G with respect to its subset S.The graph is said to be normal edge-transitive if the normalizer of G in the automorphism group Aut(T)of F acts transitively on the edge set... Let Г=Cay(G,S)be the Cayley graph of a group G with respect to its subset S.The graph is said to be normal edge-transitive if the normalizer of G in the automorphism group Aut(T)of F acts transitively on the edge set of ГIn this paper,we study the structure of normal edge-transitive Cayley graphs on a class of non-abelian groups with order 2p^(2)(p refers to an odd prime).The structure and automorphism groups of the non-abelian groups are first presented,and then the tetravalent normal edge-transitive Cayley graphs on such groups are investigated.Finally,the normal edge-transitive Cayley graphs on group G are characterized and classified. 展开更多
关键词 Cayley graph symmetric graph normal edge-transitivity
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EQGraphNet:Advancing single-station earthquake magnitude estimation via deep graph networks with residual connections
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作者 Zhiguo Wang Ziwei Chen Huai Zhang 《Artificial Intelligence in Geosciences》 2024年第1期257-268,共12页
Magnitude estimation is a critical task in seismology,and conventional methods usually require dense seismic station arrays to provide data with sufficient spatiotemporal distribution.In this context,we propose the Ea... Magnitude estimation is a critical task in seismology,and conventional methods usually require dense seismic station arrays to provide data with sufficient spatiotemporal distribution.In this context,we propose the Earthquake Graph Network(EQGraphNet)to enhance the performance of single-station magnitude estimation.The 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 signals.Our work uses the STanford EArthquake Dataset for model training and performance testing.Compared with three existing deep learning models,EQGraphNet demonstrates improved accuracy for both local magnitude and duration magnitude scales.To 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 ratios.Additionally,by replacing various network components and comparing their estimation performances,we illustrate the contribution of each part of EQGraphNet,validating the rationality of our approach.We also demonstrate the generalization capability of our model across different earthquakes occurring environments,achieving mean errors of±0.1 units.Furthermore,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. 展开更多
关键词 Magnitude estimation graph neural network symmetric graph Single-station seismic signals
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Semisymmetric Cubic Graphs as Regular Covers of K_(3,3)
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作者 Chang Qun WANG Tie Sheng CHEN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第3期405-416,共12页
A regular graph X is called semisymmetric if it is edge-transitive but not vertex-transitive. For G ≤ AutX, we call a G-cover X semisymmetric if X is semisymmetric, and call a G-cover X one-regular if Aut X acts regu... A regular graph X is called semisymmetric if it is edge-transitive but not vertex-transitive. For G ≤ AutX, we call a G-cover X semisymmetric if X is semisymmetric, and call a G-cover X one-regular if Aut X acts regularly on its arc-set. In this paper, we give the sufficient and necessary conditions for the existence of one-regular or semisymmetric Zn-Covers of K3,3. Also, an infinite family of semisymmetric Zn×Zn-covers of K3,3 are constructed. 展开更多
关键词 semisymmetric graph symmetric graph covering graph one-regular graph
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On Symmetric Cayley Graphs of Valency Eleven
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作者 Bo Ling Bengong Lou +1 位作者 Li Ma Xue Yu 《Algebra Colloquium》 SCIE CSCD 2021年第2期309-318,共10页
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,whe... 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 constructed.This 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. 展开更多
关键词 nonabelian simple group normal Cayley graph symmetric graph
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Normality of Tetravalent Cayley Graphs of Odd Prime-cube Order and Its Application 被引量:3
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作者 Yan Quan FENG Ming Yao XU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第4期903-912,共10页
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
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Automorphisms of Maps with a Given Underlying Graph and Their Application to Enumeration 被引量:2
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作者 LinFanMAO YanPeiLIU FengTIAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2005年第2期225-236,共12页
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 t... 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. 展开更多
关键词 EMBEDDING map cayley graph circulant graph symmetric graph automorphismgroup burnside lemma
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(G, s)-Transitive Graphs of Valency 7 被引量:2
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作者 Songtao Guo Yantao Li Xiaohui Hua 《Algebra Colloquium》 SCIE CSCD 2016年第3期493-500,共8页
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 ... 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. 展开更多
关键词 symmetric graph s-transitive graph (G s)-transitive graph
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Cubic one-regular graphs of order twice a square-free integer
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作者 ZHOU JinXin FENG YanQuan 《Science China Mathematics》 SCIE 2008年第6期1093-1100,共8页
A graph is one-regular if its automorphism group acts regularly on the set of its arcs. Let n be a square-free integer. In this paper, we show that a cubic one-regular graph of order 2n exists if and only if n = 3 t p... A graph is one-regular if its automorphism group acts regularly on the set of its arcs. Let n be a square-free integer. In this paper, we show that a cubic one-regular graph of order 2n exists if and only if n = 3 t p 1 p 2···p s ? 13, where t ? 1, s ? 1 and p i ’s are distinct primes such that 3| (p i ? 1). For such an integer n, there are 2 s?1 non-isomorphic cubic one-regular graphs of order 2n, which are all Cayley graphs on the dihedral group of order 2n. As a result, no cubic one-regular graphs of order 4 times an odd square-free integer exist. 展开更多
关键词 one-regular graph symmetric graph Cayley graph 05C25 20B25
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On Automorphisms of Distance-Regular Graph with Intersection Array{18,15,9;1,1,10}
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作者 A.A.Makhnev D.V.Paduchikh 《Communications in Mathematics and Statistics》 SCIE 2015年第4期527-534,共8页
Recently,Makhnev and Nirova found intersection arrays of distance-regular graphs withλ=2 and at most 4096 vertices.In the case of primitive graphs of diameter 3 withμ=1 there corresponding arrays are{18,15,9;1,1,10}... Recently,Makhnev and Nirova found intersection arrays of distance-regular graphs withλ=2 and at most 4096 vertices.In the case of primitive graphs of diameter 3 withμ=1 there corresponding arrays are{18,15,9;1,1,10},{33,30,8;1,1,30}or{39,36,4;1,1,36}.In this work,possible orders and subgraphs of fixed points of the hypothetical distance-regular graph with intersection array{18,15,9;1,1,10}are studied.In particular,graph with intersection array{18,15,9;1,1,10}is not vertex symmetric. 展开更多
关键词 Distance-regular graph AUTOMORPHISM Vertex symmetric graph
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