Let G = (V, E), V = {1, 2,. .. , n}, E = {e 1 , e 2 ,. .. , e m }, be a simple graph with n vertices and m edges. Denote by d 1 ≥ d 2 ≥ · · · ≥ d n > 0, and d(e 1) ≥ d(e 2) ≥ · · · ≥ d(e m), sequences of vertex and edge degrees, respectively. If i-th and j-th vertices of G are adjacent, it is denoted as i ∼ j. Graph invariants referred to as the first, second and the first reformulated Zagreb indices are defined as M 1 = ∑ n i=1 d 2 i , M 2 = ∑ i∼ j d i d j and EM 1 = ∑ m i=1 d(e i) 2 , respectively. Let λ 1 ≥ λ 2 ≥ · · · ≥ λ n be eigenvalues of G. With ρ(G) = λ 1 a spectral radius of G is denoted. Lower bounds for invariants M 1 , M 2 , EM 1 and ρ(G) are obtained.