Shin Min Kang

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.

Hermite Hadamard Type Inequalities for Functions Whose Derivatives Are η- Convex via Fractional Integrals

Since the Hermite–Hadamard inequality and fractional integrals have a wide range of applications, many researchers extend their studies to Hermite–Hadamard-type inequalities involving fractional integrals. In 2015, Iscan [2] obtained Hermite–Hadamard–Fejér-type inequalities for convex functions via fractional integrals. In 2017, Farid and Tariq [3] developed fractional integral inequalities for m-convex functions. Also, Farid and Abbas [4] established Hermite– Hadamard–Fejér-type inequalities for p-convex functions via generalized fractional integrals. For recent generalizations, we refer to [5–7], and [8].

Topological Indices of Carbon Graphite and Crystal Cubic Carbon Structures via M Polynomials

Graph theory plays a crucial role in modeling and designing of chemical structure or chemical network. Chemical Graph theory helps to understand the molecular structure of molecular graph. The molecular graph consists of atoms as vertices and bonds as edges. Topological indices capture symmetry of molecular structures and give it a mathematical language to predict properties such as boiling points, viscosity, the radius of gyrations etc. In this article, we study the chemical graph of carbon Crystal structure of graphite and cubic carbon and compute several degreebased topological indices. Firstly we compute M-Polynomials of these structures and then from these M-polynomials we recover nine degree-based topological indices.

Zagreb Polynomials and Redefined Zagreb Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

1. Department of Mathematics, Dong A University, Korea; yckwun@dau.ac.kr 2. Department of Mathematics, University of Management and Technology, Lahore Pakistan; abaid.math@gmail.com 3. Department of Mathematics, Division of Science and Technology, University of Education Lahore Pakistan 4. School of Information Science and Technology, Yunnan Normal University, Kunming 650500, China; gaowei@ynnu.edu.cn 5. Department of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Korea, smkang@gnu.ac.kr

Hadamard and Fejér–Hadamard inequalities for extended generalized fractional integrals involving special functions

In this paper we prove the Hadamard and the Fejér–Hadamard inequalities for the extended generalized fractional integral operator involving the extended generalized Mittag-Leffler function. The extended generalized Mittag-Leffler function includes many known special functions. We have several such inequalities corresponding to special cases of the extended generalized Mittag-Leffler function. Also there we note the known results that can be obtained.

On Generalized Moduli of Quasi-Banach Space

We shall discuss three generalized moduli such as generalized modulus of convexity, modulus of smoothness, and modulus of Zou-Cui of quasi-Banach spaces and give some important properties of these moduli. Furthermore, we establish relationships of these generalized moduli with each other.

Some Recurrence Relations and Hilbert Series of Right-Angled Affine Artin Monoid

We find the Hilbert series of the right-angled affine Artin monoid . We also discuss its recurrence relation and the growth rate.

M-Polynomials and Degree-Based Topological Indices of Triangular, Hourglass, and Jagged-Rectangle Benzenoid Systems

Chemical graph theory is a branch of mathematical chemistry which has an important effect on the development of the chemical sciences. The study of topological indices is currently one of the most active research fields in chemical graph theory. Topological indices help to predict many chemical and biological properties of chemical structures under study. The aim of this report is to study the molecular topology of some benzenoid systems. M-polynomial has wealth of information about the degree-based topological indices. We compute M-polynomials for triangular, hourglass, and jagged-rectangle benzenoid systems, and from these M-polynomials, we recover nine degree-based topological indices. Our results play a vital role in pharmacy, drug design, and many other applied areas.