Integral Cayley Graphs over Finite Groups  

作　　者：Elena VKonstantinova Daria Lytkinat 

机构地区：[1]Sobolev Institute of Mathematics,Ak.Koptyug av.4,Novosibirsk 630090,Russia [2]Novosibirsk State University,Pirogova,str.2,Novosibirsk 630090,Russia [3]Siberian State University of Telecommunications and Information Sciences Kirova str.86,Novosibirsk 630108,Russia [4]Novosibirsk State University,Pirogova str.2,Novosibirsk 630090,Russia

出　　处：《Algebra Colloquium》2020年第1期131-136,共6页代数集刊（英文版）

基　　金：The work was supported by the Program of Fundamental Scientific Research of the SB RAS N 1.5.1,project No.0314-2019-0016.

摘　　要：We prove that the spectrum of a Cayley graph over a finite group with a normal generating set S containing with every its element s all generators of the cyclic group(s)is integral.In particular,a Cayley graph of a 2-group generated by a normal set of involutions is integral.We prove that a Cayley graph over the symmetric group of degree n no less than 2 generated by all transpositions is integral.We find the spectrum of a Cayley graph over the alternating group of degree n no less than 4 with a generating set of 3-cycles of the form(k i j)with fixed k,a s{-n+1,1-n+1,2^2-n+1,...,(n-1)2-n+1}.

关 键 词：Cayley graph symmetric group alternating group group algebra Star graph 

分 类 号：O15[理学—数学]