In this paper, we consider the relations between three degree-based graph invariants, namely, the second Zagreb index M2(G), forgotten index F(G) and Lanzhou index Lz(G) for a general graph G and a tree T. We prove that for a graph G with independence number α(G), there exists [Formula presented]≤M2(G)≤[Formula presented] with both equalities holding if and only if G is the complete graph or empty graph. Moreover, we prove that for a tree T, there exists M2(T)≤[Formula presented] with equality if an...
