SHARP BOUNDS FOR THE FIRST ZAGREB INDEX AND FIRST ZAGREB COINDEX.

Let G be an undirected connected graph with n; n ⩾ 2, vertices and m edges with vertex degrees Δ = d1 ⩾ d2 ⩾ … ⩾ dn =δ. Lower and upper bounds of a graph invariants M1 = Σni =1 d2 i , referred to as the first Zagreb index, and M1 = Σ i×j (di +dj), named the first Zagreb coindex, depending on parameters n, m, Δ and δ are obtained. The obtained results represent improvement of the results reported in the literature. [ABSTRACT FROM AUTHOR]