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A topological index is a branch of chemical graph theory that is vital to analyzing the physio-chemical characteristics of chemical compound structures divided into a degree-based molecular structure such as Zagreb indices, a distance-based molecular structure such as Wiener index, and a mixed such as Gutman index. In this paper, some definitions, results, and examples of Wiener polynomial and index for subdivision graph of friendship, and bifriendship graphs, line subdivision graph of friendship, and bifriendship graphs were introduced. Moreover, we used the MATLAB program to calculate the Wiener polynomial and index of these graphs and refer to some applications. [ABSTRACT FROM AUTHOR]

Topological index is a numeric parameter obtained from the molecular graphs and is used in the study of quantitative structure property relationships (QSPR) and quantitative structure activity relationships (QSAR). Dendrimers are synthetic 3-dimensional, highly branched, monodisperse macromolecules and are considered a building block in nanotechnology with a variety of suitable applications. In this paper, we compute hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, first Zagreb polynomial and the second Zagreb polynomial of three infinite classes of nanostar dendrimers, namely NS3[n], NS4[n] and NS5[n]. [ABSTRACT FROM AUTHOR]

The topological indices are numerical invariants associated to a graph which describe its molecular topology. In QSAR/QSPR study, the Zagreb indices and Zagreb polynomials are used to predict the bioactivity of different chemical compounds. They also correlate the certain physicochemical properties of the chemical compounds. In this paper, we compute the closed formulas of the first and second Zagreb indices and their variants and their Zagreb polynomials for the two classes of perylenediimide-cored (PDI-cored) dendrimers. [ABSTRACT FROM AUTHOR]

With the help of topological index (TI) we can guess different properties of molecular structures. TI enables us to associate a number with a molecular structure. Numerous compounds can be transformed into different shapes like trees, cycles, etc. This paper is about the reverse Zagreb indices, hyper reverse Zagreb indices and their polynomials for metal-organic networks. [ABSTRACT FROM AUTHOR]

In this paper, we discuss relations among Zagreb polynomials of a graph G and generalized xyz-point-line transformation graphs Txyz(G) when z = −. Zagreb polynomials of xyz-point-line transformation graphs are obtained in terms of Zagreb polynomials of the graph G. [ABSTRACT FROM AUTHOR]

Gutman and Trinajstić (1972) defined the connection-number based Zagreb indices, where connection number is degree of a vertex at distance two, in order to find the electron energy of alternant hydrocarbons. These indices remain symmetric for the isomorphic (molecular) networks. For the prediction of physicochemical and symmetrical properties of octane isomers, these indices are restudied in 2018. In this paper, first and second Zagreb connection coindices are defined and obtained in the form of upper bounds for the resultant networks in the terms of different indices of their factor networks, where resultant networks are obtained from two networks by the product-related operations, such as cartesian, corona, and lexicographic. For the molecular networks linear polynomial chain, carbon nanotube, alkane, cycloalkane, fence, and closed fence, first and second Zagreb connection coindices are computed in the consequence of the obtained results. An analysis of Zagreb connection indices and coindices on the aforesaid molecular networks is also included with the help of their numerical values and graphical presentations that shows the symmetric behaviour of these indices and coindices with in certain intervals of order and size of the under study (molecular) networks. [ABSTRACT FROM AUTHOR]