The study of an infinite class of dendrimer nanostars by topological index approaches

Abstract

A topological index for a molecular graph G is a numeric quantity invariant under automorphisms of G. A dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers. In this article an infinite class of dendrimer nanostars is investigated under three topological indices containing PI, Szeged and edge Szeged.

Cut method for the multivariable Szeged‐like polynomial with application to hyaluronic acid

“…On the other hand, various graph polynomials corresponding to Szeged‐like topological indices have been introduced. These include, for example, the Szeged polynomial [16], the Mostar polynomial [17], the PI polynomial [18], the edge‐Szeged polynomial [19], and so forth. The mentioned graph polynomials provide valuable tools for characterizing and analysing the structural properties of graphs, offering insights into their complexity, since they provide more information about the considered graph than the index.…”

Computing eccentric connectivity index of nanostar dendrimers

“…Each successive repeat unit along all branches forms the next generation, 1 st generation and 2 nd generation and so on until the terminating generation. The topological study of these macromolecules is the aim of following articles, see (Khoramdel et al, 2008;Ashrafi et al, 2008;Karbasioun et al, 2009;Yousefi-Azari et al, 2008) for details. Now, we introduce some notation and terminology.…”

Some variants of the Szeged index under rooted product of graphs

“…We refer the reader to [1,10,14] for more information on these indices. The rooted product G 1 fG 2 g of a graph G 1 and a rooted graph G 2 is the graph obtained by taking one copy of G 1 and jV .G 1 /j copies of G 2 , and by identifying the root vertex of the i-th copy of G 2 with the i-th vertex of G 1 , for i D 1; 2; :::; jV .G 1 /j.…”