Recently, nano structures have opened new dimensions in industry, electronics, and pharmaceutical and biological therapeutics The topological graph indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physio-chemical properties such as boiling point, stability, and strain energy, of respective nano-material In this article, we established closed forms of various degree-based topological graph indices of nano-structures of 2D-lattice, nano-tube and nano-torus of TUC4C8[r,s]

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Operations of Nanostructures via SDD, ABC4 and GA5 indices

The molecular topological indices as validly demonstrated its high performance in the discovery and design of new drugs.
The goal of this paper is to study the structurally constructed a graph model of human Liver using graph operator. After the
construction, nurtured the model using various topological indices. Also, established a diagnosis defect in the human Liver.
Basically, considered structure of Liver can divide into healthy Liver and affected Liver. In this case study the topological
indices are used in describe the structure of Liver using graph operator. Constructed model can be useful further in the
medical field for any diagnosis with special care

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Reckoning of the Dissimilar Topological indices of Human Liver

The numerical descriptor gathers the data from the molecular graphs and helps to know the characteristics of the chemical structure known as topological index. The QSAR/QSPR/QSTR studies are benefited with the significant role played by topological indices in the drug design. Topological indices provide the information about the physical/chemical/biological properties of chemical compounds. The Zagreb indices are widely studied because of their extensive usage in chemical graph theory. Inspired by the earlier work on inverse sum indeg index (ISI index), novel topological index known as SS index is introduced and computed for four dendrimer structures. Also, the strong correlation coefficient between SS index and 5 physico-chemical characteristics such as boiling point (bp), molar volume (mv), molar refraction (mr), heats of vaporization (hv), and critical pressure (cp) of 67 alkane isomers have been determined. It is found that newly introduced index has shown good correlation in comparison with three most popular existing indices (ISI index and first and second Zagreb indices). In the last part, the mathematical properties of SS index are discussed.

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Computing SS Index of Certain Dendrimers

Quantitative structure–property relationship of edge weighted and degree-based entropy of benzene derivatives

Edge version of harmonic index and harmonic polynomial of some classes of graphs

Graph entropies of porous graphene using topological indices

A molecular structure can be described by a parameter, polynomial or matrix. The physico-chemical features, bio-activities of a chemical compound are predicted using the numerical descriptor called topological index. Topological indices remodel the data of molecular graphs into numerical characteristics which in turn improvises the discussion of structure property and activity relationship. The present work concentrates on obtaining the M-polynomial and NM-polynomial of porous graphene structure. Using these polynomials as tools, certain degree-based topological indices are retrieved. The applications of porous graphene are in the field of electrochemical energy storage, electrochemical sensor, electro-catalysis, DNA sequencing, biosensors and diagnostics.

M-polynomial and neighborhood M-polynomial methods for topological indices of porous graphene

The most significant tool of mathematical chemistry is the numerical descriptor called topological index. Topological indices are extensively used in modelling of chemical compounds to analyse the studies on quantitative structure activity/property/toxicity relationships and combinatorial library virtual screening. In this work, an attempt is made in defining three novel descriptors, namely, neighborhood geometric-harmonic, harmonic-geometric, and neighborhood harmonic-geometric indices. Also, the aforementioned three indices along with the geometric-harmonic index are tested for physicochemical properties of octane isomers using linear regression models and computed for some carbon nanotubes.

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Novel Degree-Based Topological Descriptors of Carbon Nanotubes

Let G be a simple graph, the vertex-set and edge-set of which are represented by V (G) and E(G) respectively. In this paper, the Harmonic indices of cubic polyhedral graphs using bridge graphs and the relations among them have been found. 4246 V. Lokesha, A. Usha, P. S. Ranjini and T. Deepika Mathematics Subject Classification: 05C05, 05C12

A. Usha

Papers

Graph entropies of porous graphene using topological indices

M-polynomial and neighborhood M-polynomial methods for topological indices of porous graphene

Computing SS Index of Certain Dendrimers

Novel Degree-Based Topological Descriptors of Carbon Nanotubes

Harmonic index of cubic polyhedral graphs using bridge graphs