Journal of Algebraic Combinatorics

, Volume 47, Issue 4, pp 585–601 | Cite as

Integral Cayley graphs over dihedral groups



In this paper, we give a necessary and sufficient condition for the integrality of Cayley graphs over the dihedral group \(D_n=\langle a,b\mid a^n=b^2=1,bab=a^{-1}\rangle \). Moreover, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over \(D_n\) in terms of the Boolean algebra of \(\langle a\rangle \), from which we find infinite classes of integral Cayley graphs over \(D_n\). In particular, we completely determine all integral Cayley graphs over the dihedral group \(D_p\) for a prime p.


Cayley graph Integral graph Dihedral group Character 

Mathematics Subject Classification




The authors would like to thank the referees and the editors for very careful reading and for helpful comments which helped to improve the presentation of the paper.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.College of Mathematics and Systems ScienceXinjiang UniversityÜrümqiPeople’s Republic of China

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