Fixed-Order Chemical Trees with Given Segments and Their Maximum Multiplicative Sum Zagreb Index

Abstract

Topological indices are often used to predict the physicochemical properties of molecules. The multiplicative sum Zagreb index is one of the multiplicative versions of the Zagreb indices, which belong to the class of most-examined topological indices. For a graph G with edge set E={e1,e2,⋯,em}, its multiplicative sum Zagreb index is defined as the product of the numbers D(e1),D(e2),⋯,D(em), where D(ei) is the sum of the degrees of the end vertices of ei. A chemical tree is a tree of maximum degree at most 4. In this research work, graphs possessing the maximum multiplicative sum Zagreb index are determined from the class of chemical trees with a given order and fixed number of segments. The values of the multiplicative sum Zagreb index of the obtained extremal trees are also obtained.

Keywords

• topological index
• multiplicative sum Zagreb indices
• chemical trees
• segments
• extremal problem