Abstract
The irregularity of a graph G is defined as irr(G) = Sigma(uv epsilon E(G)) vertical bar d(u) - d(v)vertical bar, where d(u) denotes the degree of a vertex u epsilon V (G) and E(G) is the edge set of G. From the class of all n-vertex (molecular) trees, graphs with the first five minimal irr-values have already been characterized in the literature. The main purpose of this paper is to determine the graphs with the sixth, seventh and eighth minimal irr-values among all the members of the aforementioned class for n >= 7, n >= 8 and n >= 8, respectively.