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 〈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, as {−n+1, 1−n+1, 22 −n+1, …, (n−1)2 −n+1}.
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2019 ◽
Vol 18
(01)
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pp. 1950013
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2011 ◽
Vol 2011
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pp. 1-16
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2019 ◽
Vol 29
(08)
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pp. 1419-1430
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