Integral Cayley graphs over dihedral groups

By Lu Lu, Qiongxiang Huang, Xueyi Huang. 2016

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In this paper, we give a necessary and sufficient condition for the integrality of Cayley graphs over the dihedral group $$D_n=\langle a,b\mid a^n=b^2=1,bab=a^{-1}\rangle $$Dn=⟨a,b∣an=b2=1,bab=a-1⟩. Moreover, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over $$D_n$$Dn in terms of the Boolean algebra of $$\langle a\rangle $$⟨a⟩, from which we find infinite classes of integral Cayley graphs over $$D_n$$Dn. In particular, we completely determine all integral Cayley graphs over the dihedral group $$D_p$$Dp for a prime p.

Subfields: Discrete Mathematics and Combinatorics, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/992c7fbdbde7707a134bd642e648e7cf23e67112