M-Polynomials and Topological Indices of Titania Nanotubes

Abstract

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 TiO 2 ) nanotubes and recover important topological degree-based indices to theoretically judge these nanotubes. We also plot surfaces associated to single-walled titania (SW TiO 2 ) nanotubes.

M-Polynomials and Degree-Based Topological Indices of Bismuth Tri-Iodide

“…[15], in the context of degree-based indices. Authors in [15] introduced M-polynomial in, 2015, to play a role, parallel to Hosoya polynomial to determine closed form of many degree-based topological indices [16][17][18][19][20]. The real power of M-polynomial is its comprehensive nature containing healthy information about degree-based graph invariants.…”

“…Tables presented in [15][16][17][18][19] relates some of these well-known degree-based topological indices with M-polynomial with following reserved notations ( )…”

Some Computational Aspects of Boron Triangular Nanotubes

“…Algebraic polynomials have also useful applications in chemistry, such as Hosoya polynomial (also called Wiener polynomial) [8], which plays a vital role in determining distance-based topological indices. Among other algebraic polynomials, the M-polynomial [9], introduced in 2015, plays the same role in determining the closed form of many degree-based topological indices [10][11][12][13][14]. The main advantage of M-polynomial is the wealth of information that it contains about degree-based graph invariants.…”

Some Algebraic Polynomials and Topological Indices of Octagonal Network

“…From this M-polynomial, we can calculate many topological indices. M-polynomial of different molecular structures has been computed in [9][10][11][12]. The topological index of a molecule structure can be considered as a non-empirical numerical quantity which quantifies the molecular structure and its branching pattern in many ways.…”