Relations between degree-based graph invariants

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 alpha(G), there exists F(G)- Lz(G) F(G) + Lz(G) 2 alpha(G) <= M2(G) <= 2 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 F(T) + Lz(T) M2(T) <= 3 with equality if and only if T is the path of order 3.(c) 2022 Elsevier B.V. All rights reserved.