Integral Cayley Graphs over Finite Groups

• 来源期刊: 代数集刊（英文版）
• 关键词: Cayley graph symmetric group alternating group group algebra Star graph
• 年，卷（期）: 2020,（1）
• 页码范围: 131-136
• 页数: 6页
• 语种: 英文
• DOI: 10.1142/S1005386720000115

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 (kij) with fixed k,as {-n+1,1-n+1,22-n+1,...,(n-1)2-n+1}.