The modified first Zagreb connection index and the trees with given order and size of matchings

Abstract

A subset of the edge set of a graph G is called a matching in G if its elements are not adjacent in G. A matching in G with the maximum cardinality among all the matchings in G is called a maximum matching. The matching number in the graph G is the number of elements in the maximum matching of G. This present paper is devoted to the investigation of the trees, which maximize the modified first Zagreb connection index among the trees with a given order and matching number.