We compute the degree of Hurwitz-Hodge classes $λ_1^e$ on one dimensional moduli spaces of cyclic admissible covers of the projective line. We also compute the degree of the the first Chern class of the Hodge bundle $λ_1$ for all one dimensional moduli spaces. In higher dimension, we express the divisor class $λ_1$ as a linear combination of $ψ$ classes and boundary strata.