TREES WITH THE MINIMAL SECOND ZAGREB INDEX

For simple graph G with edge set E(G), the second Zagreb index of G is defined as M-2(G) = Sigma(uv is an element of E(G))[d(G)(u)d(G)(v)], where d(G)(v) is the degree of the vertex v in G. In this paper, we identify the nine classes of trees, which have the first to the sixth smallest second Zagreb indices, among all the trees of the order n >= 11.