Abstract
A series of previously conducted experiments pertaining to various chemicals and drugs uncover a natural linkage between the molecular structures and the bio-medical and pharmacological characteristics. The forgotten topological index computed for the molecular structures of various chemical compounds and drugs has proven significant in medical and pharmaceutical fields by predicting biological features of new chemical compounds and drugs. A topological index can be considered as the transformation of chemical structure into a real number. Dendrimers are highly-branched star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. In this paper, we determine forgotten topological indices of poly(propyl) ether imine, porphyrin, and zinc–porphyrin dendrimers.
Highlights
We are living in an era where every day sees better innovation than the previous, with the same trend in the enhancement and innovation in the production of different types of medicines, chemical compounds, and drugs for the improved health of humans and other living species on the planet
The Zagreb index M1 was first encountered in a paper published in 1972 [1], where a series of approximate formulas for total π-electron energy E were deduced. By means of these formulas, several structural details have been identified, upon which E depends. Among these was the sum of squares of the vertex degrees of the underlying molecular graph are discussed
We consider the class of porphyrin dendrimers, denoted by Dn Pn
Summary
We are living in an era where every day sees better innovation than the previous, with the same trend in the enhancement and innovation in the production of different types of medicines, chemical compounds, and drugs for the improved health of humans and other living species on the planet. For a graph G, the degree of a vertex v is the number of edges incident with v and denoted by dv. Degree-based topological indices are the most important and widely used These have great application in chemical graph theory. Since the 1970s, two degree-based graph invariants have been extensively studied These are the first Zagreb index M1 and the second Zagreb index M2 , defined as. By means of these formulas, several structural details have been identified, upon which E depends Among these was the sum of squares of the vertex degrees of the underlying molecular graph are discussed. Let eij denote the number of edges of G connecting vertices of degrees i and j. Let us denote the number of edges connecting vertices of degrees i and j in each branch of the dendrimer by eij0.
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