Trees with the minimal second Zagreb index

Abstract

For simple graph G with edge set E(G), the second Zagreb index of G is defined as M2(G) = Σuv∈E(G)[dG(u)dG(v)], where dG(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. © University of Kragujevac - Faculty of Science, 2018.