Integral Cayley Graphs over Finite Groups

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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 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, as {-n+1, 1-n+1, 22 -n+1, ..., (n-1)2 -n+1}.

Original languageEnglish
Pages (from-to)131-136
Number of pages6
JournalAlgebra Colloquium
Issue number1
Publication statusPublished - 1 Mar 2020


  • alternating group
  • Cayley graph
  • group algebra
  • Star graph
  • symmetric group


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