Closed Formulas for Some New Degree Based Topological Descriptors Using M-polynomial and Boron Triangular Nanotube (original) (raw)
COMPUTING SOME TOPOLOGICAL INDICES OF CARBON NANOTUBES
In this paper, several topological indices are investigated for H-Phenylenic nanotube, H-Naphthylenic nanotube and H-Anthracenic nanotube. The calculated indices are product-connectivity index, sum-connectivity index, geometric-arithmetic index and atom-bond connectivity index.
Computational Analysis of topological indices of two Boron Nanotubes
Scientific Reports
There has been a recent debate that boron nanotubes can outperform carbon nanotubes on many grounds. The most stable boron nanotubes are made of a hexagonal lattice with an extra atom added to some of the hexagons called ∝-boron nanotubes. Closed forms of M-polynomial of nanotubes produce closed forms of many degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned nanotubes. In this article, we compute and analyze many topological indices of ∝-boron nanotubes correlating with the size of structure of these tubes through the use of M-polynomial. More importantly we make a graph-theoretic comparison of indices of two types of boron nanotubes namely triangular boron and ∝-boron nanotubes. Mathematical chemistry provides tools such as polynomials and functions to capture information hidden in the symmetry of molecular graphs and thus predict properties of compounds without using quantum mechanics. A topological index isa numerical parameter of a graph and depicts its topology. It describes the structure of molecules numerically and are used in the development of qualitative structure activity relationships (QSARs). Most commonly known invariants of such kinds are degree-based topological indices. These are actually the numerical values that correlate the structure with various physical properties, chemical reactivity and biological activities 1-5. It is an established fact that many properties such as heat of formation, boiling point, strain energy, rigidity and fracture toughness of a molecule are strongly connected to its graphical structure. Hosoya polynomial, (Wiener polynomial) 6 , plays a pivotal role in distance-based topological indices. A long list of distance-based indices can be easily evaluated from Hosoya polynomial. A similar breakthrough was obtained recently by Klavzar et. al. 7 , in the context of degree-based indices. Authors in 7 introduced M-polynomial in, 2015, to play a role, parallel to Hosoya polynomial to determine closed form of many degree-based topological indices 8-12. The real power of M-polynomial is its comprehensive nature containing healthy information about degree-based graph invariants. These invariants are calculated on the basis of symmetries present in the 2d-molecular lattices and collectively determine some properties of the material under observation. Because of increasing interests and developments of new nanomaterials, computations have minimized the burden of experimental labor to some extent. Amongst the nanomaterials, nanocrystals, nanowires and nanotubes, constitute three major categories, the last two being one-dimensional. Boron nanotubes are becoming increasingly interesting because of their remarkable properties like structural stability, work function, transport properties, and electronic structure 13. Triangular Boron is derived from a triangular sheet as shown in Fig. 1. The first boron nanotubes were created, in 2004, from a buckled triangular latticework 13-15. These tubes are discussed recently in 15,16. Other well-known type, α-boron, is derived from α-sheet. Irrespective of their structures and chiralities, both types are more conductive than carbon nanotubes 14,17-19. Figure 2 describes basic structure of ∝boron nanotube. Following Fig. 3 also presents different views of ∝-Boron nanotube, (a) is the planar view whereas (b) is the tabular view. As for as structure of both tubes are concerned, ∝-Boron nanotube is more complicated than Triangular boron nanotubes with addition of an extra atom to the center of some of the hexagons 15. In 15 , authors proved that this is the most stable known theoretical structure for a boron nanotube. They also showed that, with this pattern, boron nanotubes should have variable electrical properties: wider ones would be metallic conductors,
Due to the presence of multicenter bonds and their novel electronic properties, boron nanotubes are attractive. The tri-hexagonal boron nanotubes are build up from triangles and hexagons. It is useful to the QSPR/QSAR studies. Topological indices are classified in different forms such as, degree based topological indices, distance based topological indices and counting related topological indices etc. Here, we concentrated the reckoning of topological indices such as first zagreb, second zagreb, modified second zagreb index, generalized randic index, symmetric division degree index for the tri-hexagonal boron nanotube. Also, established their M-polynomials and using maple software plotted the 3D structure.
Computing Degree-Based Topological Indices of Polyhex Nanotubes
2016
Recently, Shigehalli and Kanabur [20] have put forward for new degree based topological indices, namely Arithmetic-Geometric index (AG1 index), SK index, SK1 index and SK2 index of a molecular graph G. In this paper, we obtain the explicit formulae of these indices for Polyhex Nanotube without the aid of a computer.
Some Formulas for the Polynomials and Topological Indices of Nanostructures
Acta Chemica Iasi, 2016
In this paper, we focus on the structure of Polycyclic Aromatic Hydrocarbons (PAHs) and calculate the Omega and its related counting polynomials of nanostructures. Also, the exact expressions for the Theta, Sadhana, Pi, Hyper Zagreb and Forgotten Zagreb indices of linear [n]-Tetracene, V-Tetracenic nanotube, H-Tetracenic nanotube and Tetracenic nanotori were computed for the first time. These indices can be used in QSAR/QSPR studies.
Investigation on Boron Alpha Nanotube by Studying Their M-Polynomial and Topological Indices
Journal of Mathematics
Graph theory provides an effective tool such as graph polynomial and topological indices (TIs) to the chemist to analyze the different chemical structures. TIs are the numerical entity deducted from the molecular structure. TI helps to study the relationship between the physicochemical properties and structure of the chemical compound. In this article, we investigate the boron α -nanotube by computing its M-polynomial and then deducing its TI. Results are also shown by plotting the graphs.
Computing topological polynomials of certain nanostructures
OPTOELECTRONICS AND ADVANCED MATERIALS-RAPID COMMUNICATIONS
Counting polynomials are those polynomials having at exponent the extent of a property partition and coefficients the multiplicity/occurrence of the corresponding partition. In this paper, Omega, Sadhana and PI polynomials are computed for Multilayer Hex-Cells nanotubes, One Pentagonal Carbon nanocones and Melem Chain nanotubes. These polynomials were proposed on the ground of quasi-orthogonal cuts edge strips in polycyclic graphs. These counting polynomials are useful in the topological description of bipartite structures as well as in counting some single number descriptors, i.e. topological indices. These polynomials count equidistant and non-equidistant edges in graphs. In this paper, analytical closed formulas of these polynomials for Multi-layer Hex-Cells MLH (k, d) nanotubes, One Pentagonal Carbon CNC_5 (n) nanocones and Melem Chain MC (n) nanotubes are derived.
On multiplicative degree based topological indices of singlewalled titania nanotubes
2018
A topological index is a special number which describes the whole structure of a graph. The topological indices are categorized on the basis of their logical roots from topological invariant. A topological index which depends on the degree of a vertex is called degree based topological index. In this paper we will calculate some degree based multiplicative topological indices of single-walled Titania nanotubes.
On certain degree-based topological indices of armchair polyhex nanotubes
2018
Recently [18], Shigehalli and Kanabur have introduced two new topological indices namely, AG2 index and SK3 index. Hosamani [14], has studied a novel topological index, namely the Sanskruti index S (G) of a molecular graph G. In this paper, formula for computing the armchair polyhex nanotube TUAC6 [m, n] family is given.
Computation of the different topological indices of nanostructures
In this research study, several topological indices have been investigated for linear [n]-Tetracene, V-Tetracenic nanotube, H-Tetracenic nanotube and Tetracenic nanotori. The calculated indices are first, second, third and modified second Zagreb indices. In addition, the first and second Zagreb coindices of these nanostructures were calculated. The explicit formulae for connectivity indices of various families of Tetracenic nanotubes and nanotori are presented in this manuscript. These formulae correlate the chemical structure of nanostructures to the information about their physical features.