Waqas Nazeer

M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes

The discovery of new nanomaterials adds new dimensions to industry, electronics, and pharmaceutical and biological therapeutics. In this article, we first find closed forms of M-polynomials of polyhex nanotubes. We also compute closed forms of various degree-based topological indices of these tubes. These indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties, such as boiling point, stability, and strain energy, of respective nanomaterial. To conclude, we plot surfaces associated to M-polynomials and characterize some facts about these tubes.

M-Polynomial and Related Topological Indices of Nanostar Dendrimers

Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices.

M-Polynomials and Topological Indices of Titania Nanotubes

Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produces many degree-based topological indices, which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules, such as boiling point, stability, strain energy, etc., are correlated with their structure. In this report, we provide M-polynomials of single-walled titania (SW TiO2) nanotubes and recover important topological degree-based indices to theoretically judge these nanotubes. We also plot surfaces associated to single-walled titania (SW TiO2) nanotubes.

Some Invariants of Circulant Graphs

Topological indices and polynomials are predicting properties like boiling points, fracture toughness, heat of formation, etc., of different materials, and thus save us from extra experimental burden. In this article we compute many topological indices for the family of circulant graphs. At first, we give a general closed form of M-polynomial of this family and recover many degree-based topological indices out of it. We also compute Zagreb indices and Zagreb polynomials of this family. Our results extend many existing results.

M-Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori

V-Phenylenic nanotubes and nanotori are most comprehensively studied nanostructures due to widespread applications in the production of catalytic, gas-sensing and corrosion-resistant materials. Representing chemical compounds with M-polynomial is a recent idea and it produces nice formulas of degree-based topological indices which correlate chemical properties of the material under investigation. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules like boiling point, stability, strain energy etc. are correlated with their structures. In this paper, we determine general closed formulae for M-polynomials of V-Phylenic nanotubes and nanotori. We recover important topological degree-based indices. We also give different graphs of topological indices and their relations with the parameters of structures.

Some Computational Aspects of Boron Triangular Nanotubes

The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M‐polynomial of nanotubes produces closed forms of many degree‐based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M‐polynomials of boron triangular nanotubes and recover many important topological degree‐based indices of these nanotubes. We also plot surfaces associated with these nanotubes that show the dependence of each topological index on the parameters of the structure.

M-Polynomials And Topological Indices Of Zigzag And Rhombic Benzenoid Systems

Abstract M-polynomial of different molecular structures helps to calculate many topological indices. This polynomial is a new idea and its beauty is the wealth of information it contains about the closed forms of degree-based topological indices of molecular graph G of the structure. It is a well-known fact that topological indices play significant role in determining properties of the chemical compound [1, 2, 3, 4]. In this article, we computed the closed form of M-polynomial of zigzag and rhombic benzenoid systemsbecause of their extensive usages in industry. Moreover we give graphs of M-polynomials and their relations with the parameters of structures.

On Eccentricity-Based Topological Indices and Polynomials of Phosphorus Containing Dendrimers

In the study of the quantitative structure–activity relationship and quantitative structure-property relationships, the eccentric-connectivity index has a very important place among the other topological descriptors due to its high degree of predictability for pharmaceutical properties. In this paper, we compute the exact formulas of the eccentric-connectivity index and its corresponding polynomial, the total eccentric-connectivity index and its corresponding polynomial, the first Zagreb eccentricity index, the augmented eccentric-connectivity index, and the modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

Topological aspects of some dendrimer structures

Abstract A numerical number associated to the molecular graph G that describes its molecular topology is called topological index. In the study of QSAR and QSPR, topological indices such as atom-bond connectivity index, Randić connectivity index, geometric index, etc. help to predict many physico-chemical properties of the chemical compound under study. Dendrimers are macromolecules and have many applications in chemistry, especially in self-assembly procedures and host-guest reactions. The aim of this report is to compute degree-based topological indices, namely the fourth atom-bond connectivity index and fifth geometric arithmetic index of poly propyl ether imine, zinc porphyrin, and porphyrin dendrimers.

M-polynomials and topological indices of hex-derived networks

Abstract Hex-derived network has a variety of useful applications in pharmacy, electronics, and networking. In this paper, we give general form of the M-polynomial of the hex-derived networksHDN1[n] and HDN2[n], which came out of n-dimensional hexagonal mesh. We also give closed forms of several degree-based topological indices associated to these networks.