Algebraic degree of Cayley graphs over abelian groups and dihedral groups

Source abstract

Abstract For a graph $$\Gamma$$ Γ , let K be the smallest field containing all eigenvalues of the adjacency matrix of $$\Gamma$$ Γ . The algebraic degree $$\deg (\Gamma )$$ deg ( Γ ) is the extension degree $$[K:\mathbb {Q}]$$ [ K : Q ] . In this paper, we completely determine the algebraic degrees of Cayley graphs over abelian groups and dihedral groups.