Abstract
The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.
Highlights
topological indices (TIs) are the numerical numbers which are linked with different chemical structures of molecular graphs and predict the structural, toxicological, biological, and physicochemical properties of the existing chemical compounds
Gutman and Trinajstić [22] put forward the innovative idea of the well-known TI named as first Zagreb index (FZI)
We establish the general expressions to calculate the MZCIs of two well-known dendrimer nanostars in a very logical and comprehensive way
Summary
TIs are the numerical numbers which are linked with different chemical structures of molecular graphs and predict the structural, toxicological, biological, and physicochemical properties of the existing chemical compounds. Dankelmann et al calculated the sharp upper bounds of graphs by utilizing these distance-based TIs in a very comprehensive way. Degree-based TI is further categorized into two subclasses named as degree and connection-based TIs. Gutman and Trinajstić [22] put forward the innovative idea of the well-known TI named as first Zagreb index (FZI). We rewrite some already introduced connection-based MZIs. Further, we establish the general expressions to calculate the MZCIs of two well-known dendrimer nanostars in a very logical and comprehensive way.
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