paper

Integral Cayley Graphs over Dihedral Groups

arXiv:1606.02184

Abstract

In this paper, we give a necessary and sufficient condition for the integrality of Cayley graphs over the dihedral group $D_{n} = ⟨ a, b ∣ a^{n} = b^{2} = 1, bab = a^{- 1} ⟩$ . Moreover, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over $D_{n}$ in terms of the Boolean algebra of $⟨ a ⟩$ , 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 $p$ .

15 pages. arXiv admin note: text overlap with arXiv:1307.6155 by other authors