On the minimum second Zagreb index of trees with small parameters

Abstract

The second Zagreb index M 2 is one of the oldest vertex-degree-based molecular structure descriptors, introduced in the 1970s. Recently, there has been a great interest in studying extremal graphs that minimize (or maximize) second Zagreb index in different classes of graphs. In this paper, lower bounds on the second Zagreb index of trees with given small parameters such as diameter, matching number and domination number are determined and the extremal trees are characterized, as well.