On the Multiplicative Sum Zagreb Index of Molecular Trees With Given Order and Number of Branching Vertices

The multiplicative sum Zagreb index of a graph G is defined as the product of the sum of the degrees of adjacent vertices of G. A molecular tree is an acyclic connected graph with maximum degree at most 4. A vertex in a molecular tree with degree 3 or 4 is referred to as a branching vertex. In this paper, we consider the class of all molecular trees of fixed order and with a given number of branching vertices and study the members of this class with the maximum value of the multiplicative sum Zagreb index.