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Automorphism Groups of Cubic cayley graphs of Dihedral Groups of Order 2npm(n ≥ 2 and p Odd Prime)

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Automorphism Groups of Cubic Cayley Graphs of Dihedral Group...

Reconfigurable Optical Bus and Performance Optimization

作者： Xianfen Kong Department of Foundational Mathematics Xi’an Jiaotong-Liverpool University

For a prime p,let D be the dihedral group of order 2p and Cay(G,S) be a connected cubic cayley graph on G with respect to a generating system of three elements S such that S does not contain the identity and S=*** this paper,the automorphism groups of cubic cayley graphs of dihedral groups of order 2p where n≥2 and p is odd prime are completely *** S≡{b,ab,a2p)b},the automorphism group Aut ■.Except in this case,the automorphism group Aut(Cay(G,S)) is the semidirect product R(G)■Aut(G,S) where R(G) is the right regular representation of G and Aut(G,S)={α∈Aut(G)|Sα=S}.

关键词： Automorphism Group Dihedral Group cayley graph

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Journal of Computer Science & Technology 1996年第3期11卷 296-312页

作者： SibabrataRAY 江泓 DepartmentofComputerScience＆EngineeringUniversityofNebraska－Lincoln LincolnNE68588－0115U.S.A Depart

With the advent of optical fiber and other advanced technologies in solid state,pipelining signals at the wire (or transmission line) level has become possible. This has, in turn, made the slotted bus a potential candidate for interconnection networks (IN) for tightly coupled multiprocessor systetns. However, a bus can provide only lboted bandwidth. Though slotted bus can provide considerably more bandwidth in comparison to the traditional non-slotted bus, it is not enough for fine-grain parallel applications run on the shared-memory systems. One well knowll method to increase the effective bandwidth of a slotted bus in the LAN/MAN environment is to reuse the bandwidth by reusing slots. However, in a tightly coupled environment reusing slots is not a lucrative option because the significallt buffering needs arising from slot reuse will introduce intolerable delay. In this paper we propose a methodology to reuse part of the bandwidth available from temporal and spectral bandwidth expansion with none or minimum buffering delay, resulting in significant performance improvement in both the effective throughput and response time (communication latency). The proposed method entails the design and allalysis of a re-configurable bus structure with both temporal and spectral bandwidth expansion and a polynomial time algorithm for optimal codrigurations for given traffic conditions. We have compared the performance of our reconfigured bus with that of the traditional slotted bus for uniform and localized traffic pattern and found that the recondgured bus outperforms the traditional slotted bus substalitially in many practical scenarios.

关键词： cayley graph routing diameter embedding interconnection network

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

An Addressing and Routing Scheme Based on Modified Euclidean Space for Hexagonal Networks

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China Communications 2015年第5期12卷 94-99页

作者： GONG Jiezhong LI Lin CHEN Gongliang WU Yue LI Jianhua Information Security Research Center China Electronics Standardization Institute Information Security Engineering School Shanghai Jiaotong University

The addressing and routing algorithm on hexagonal networks is still an open problem so *** many related works have been done to resolve this problem to some extent,the properties of hexagonal networks are still not explored *** this paper,we first create an oblique coordinate system and redefine the Euclidean space to address the hexagonal *** an optimal routing algorithm using vectors and angles of the redefined Euclidean space is *** with the traditional 3-directions scheme and the cayley graph method,the proposed routing algorithm is more efficient and totally independent of the scale of networks with two-tuples *** also prove that the path(s) obtained by this algorithm is always the shortest one(s).

关键词： hexagonal network euclidean space addressing routing algorithm cayley graph

On restricted edge-connectivity of replacement product graphs

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Science China Mathematics 2017年第4期60卷 745-758页

作者： HONG ZhenMu XU JunMing School of Finance Anhui University of Finance & Economics School of Mathematical Sciences University of Science and Technology of China

This paper considers the edge-connectivity and the restricted edge-connectivity of replacement product graphs, gives some bounds on edge-connectivity and restricted edge-connectivity of replacement product graphs and determines the exact values for some special graphs. In particular, the authors further confirm that under certain conditions, the replacement product of two cayley graphs is also a cayley graph, and give a necessary and sufficient condition for such cayley graphs to have maximum restricted edge-connectivity. Based on these results, we construct a cayley graph with degree d whose restricted edge-connectivity is equal to d + s for given odd integer d and integer s with d 5 and 1 s d- 3, which answers a problem proposed ten years ago.

关键词： graph theory connectivity restricted edge-connectivity replacement product cayley graph

On the Classification of Arc-transitive Circulant Digraphs of Order Odd-Prime-Squared

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Acta Mathematica Sinica,English Series 2005年第5期21卷 1131-1136页

作者： Xue Wen LI LMAM & School of Mathematical Sciences Peking University Beijing 100871 P. R. China Department of Mathematics Tangshan Teacher's College Tangshan 063000 P. R. China

A cayley graph F = Cay（G, S） of a group G with respect to S is called a circulant digraph of order pk if G is a cyclic group of the same order. Investigated in this paper are the normality conditions for arc-transitive circulant （di）graphs of order p^2 and the classification of all such graphs. It is proved that any connected arc-transitive circulant digraph of order p^2 is, up to a graph isomorphism, either Kp2, G（p^2,r）, or G（p,r）[pK1], where r｜p- 1.

关键词： cayley graph Normal cayley graph Circulant digraph

On Non-normal Arc-Transitive 4-Valent Dihedrants

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Acta Mathematica Sinica,English Series 2010年第8期26卷 1485-1498页

作者： István KOVCS Botjan KUZMAN Aleksander MALNI FAMNIT University of Primorska PeF University of Ljubljana IMFM University of Ljubljana

Let X be a connected non-normal 4-valent arc-transitive cayley graph on a dihedral group Dn such that X is bipartite, with the two bipartition sets being the two orbits of the cyclic subgroup within Dn. It is shown that X is isomorphic either to the lexicographic product Cn[2K1] with n 〉 4 even, or to one of the five sporadic graphs on 10, 14, 26, 28 and 30 vertices, respectively.

关键词： cayley graph arc transitivity dihedral group

Cubic one-regular graphs of order twice a square-free integer

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Science China Mathematics 2008年第6期51卷 1093-1100页

作者： ZHOU JinXin FENG YanQuan Department of Mathematics Beijing Jiaotong UniversityBeijing 100044China

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.

关键词： one-regular graph symmetric graph cayley graph 05C25 20B25

A NEW FAMILY OF TRIVALENT cayley NETWORKS ON WREATH PRODUCT Z_m■S_n

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Journal of Systems Science & Complexity 2006年第4期19卷 577-585页

作者： Shuming ZHOU Key Laboratory of Network Security and Cryptology(Fujian Normal University),Fujian Province University,Fuzhou,350007 College of Mathematics and Computer Science,Fajian Normal University,Fuzhou,350007,China. Key Laboratory of Network Security and Cryptology (Fujian Normal University) Fujian Province University Fuzhou College of Mathematics and Computer Science Fujian Normal University Fuzhou China

We propose a new family of interconnection networks （WGn^m） with regular degree three. When the generator set is chosen properly, they are isomorphic to cayley graphs on the wreath product Zm ～ Sn. In the case of m ≥ 3 and n ≥3, we investigate their different algebraic properties and give a routing algorithm with the diameter upper bounded by [m/2]（3n^2- 8n ＋ 4） - 2n ＋ 1. The connectivity and the optimal fault tolerance of the proposed networks are also derived. In conclusion, we present comparisons of some familiar networks with constant degree 3.

关键词： cayley graph connectivity diameter interconnection network routing