Normalized Laplacian polynomial of n-Cayley graphs.

Let G be a finite group and Γ be a (di)graph. Then Γ is called an n-Cayley (di)graph over G if Aut (Γ) admits a semiregular subgroup isomorphic to G with n orbits on V (Γ). In this paper, we determine the normalized Laplacian polynomial of n-Cayley (di)graphs over a group G in terms of irreducible representations of G. We give exact formulas for the normalized Laplacian eigenvalues of 2-Cayley graphs over abelian groups. Among other results, as an application, we prove that the degree-Kirchhoff index of the n-sunlet graph is n (2 n − 1) (2 n + 7) 3 . [ABSTRACT FROM AUTHOR]