Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices  

作　　者：Istvan KOVACS 

机构地区：[1]UP IAM&FAMNIT,University of Primorska,Muzejski trg 2,6000 Koper,Slovenia

出　　处：《Acta Mathematica Sinica,English Series》2023年第4期618-632,共15页数学学报（英文版）

基　　金：Supported by the Slovenian Research Agency (research program P1-0285 and research projects N1-0062,J1-9108,J1-1695,N1-0140,J1-2451,N1-0208 and J1-3001)。

摘　　要：We show that,up to isomorphism,there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n≥4.This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs(Discrete Math.,256,301-334(2002)).As an application,a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups,which generalises the earlier formula of Huang et al.dealing with the particular case when n is a prime(Acta Math.Sin.,Engl.Ser.,33,996-1011(2017)).As another application,a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve(arXiv preprint,(2007)).

关 键 词：Cayley graph graph isomorphism dihedral group circulant matrix 

分 类 号：O157.5[理学—数学]