On linear combinations between Zagreb indices/coindices of a line graph

Let g = (v,e), v = {v1,v2, . . . ,vn}, be a simple graph of order n and size m. denote by δ = d1 ≥ d2 ≥ · · · ≥ dn = δ, di = d(vi), and δ_e = d(e1) ≥ d(e2) ≥ · · · ≥ d(e_m) = δ_e, sequences of vertex and edge degrees, respectively. the first reformulated zagreb index (coindex) is defined as em1(g) = σ ^m_i=1 d(e_i)² = σ _e_i∼e_j (d(e_i) + d(e_j)) em1(g) = σ _e_i≁e_j (d(e_i) + d(e_j)) . we consider relationship between reformulated zagreb indices/coindices and determine their bounds in terms of some basic graph parameters.