M-Polynomials and Associated Topological Indices of Sodalite Materials

Abbas, Ghazanfar; Ibrahim, Muhammad; Ahmad, Ali; Azeem, Muhammad; Elahi, Kashif

doi:10.1155/2021/5924409

Cited by 6 publications

(4 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this subsection, we have defined some formulas and some basics of the topics. Definition 1.1 16 "Hosoya polynomials, the most well-known and first, were initially released by 17 in 1988, and modified polynomials which are called modified-polynomial were introduced by 16,18 in 2015. A strong connection exists between this type of polynomial and degree-based topological indices.…”

Section: Preliminariesmentioning

confidence: 99%

Applications of magnesium iodide structure via modified-polynomials

Ghazwani,

Jamil,

Ahmad

et al. 2024

Sci Rep

Self Cite

View full text Add to dashboard Cite

A relatively recent approach in molecular graph theory for analyzing chemical networks and structures is called a modified polynomial. It emphasizes the characteristics of molecules through the use of a polynomial-based procedure and presents numerical descriptors in algebraic form. The Quantitative Structure-Property Relationship study makes use of Modified Polynomials (M-Polynomials) as a mathematical tool. M-Polynomials used to create connections between a material’s various properties and its structural characteristics. In this study, we calculated several modified polynomials and gave a polynomial description of the magnesium iodide structure. Particularly, we computed first, second and modified Zagreb indices based M-polynomials. Randić index, and inverse Randić indices based M-polynomials are also computed in this work.

show abstract

Section: Preliminariesmentioning

confidence: 99%

Applications of magnesium iodide structure via modified-polynomials

Ghazwani,

Jamil,

Ahmad

et al. 2024

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…M-polynomials are associated with degree-based indices [22][23][24][25][26][27][28][29][30][31] whereas CoM-polynomials with that of non-adjacency vertices [32].…”

Section: Com-polynomialmentioning

confidence: 99%

“…As the non‐adjacent vertices consume a lot of time for calculations, a new concept of coindices is introduced. M‐polynomials are associated with degree‐based indices [22–31] whereas CoM‐polynomials with that of non‐adjacency vertices [32]. Definition For a simple connected graph G , the CoM‐polynomial is defined as,

italicCoM ((), G; x, y) goodbreak= \overset{M}{true} ((), G; x, y) goodbreak= \sum_{i \leq j} {\overset{true¯}{m}}_{ij} ((), G) x^{i} y^{j}

where

{\overset{true¯}{m}}_{ij}, i, j \geq 1

represents the number of edges ab ∉ E ( G ) such that { d ( a ), d ( b )} = { i , j }.…”

Section: Com‐polynomialmentioning

confidence: 99%

Comparative study of chitosan derivatives through CoM‐polynomial

Shanmukha¹,

Usha

2022

Int J of Quantum Chemistry

View full text Add to dashboard Cite

Most abundant polysaccharides having numerous applications in biopolymers, bioscience and other fields are chitin and chitosan. Hydrogels are their derivatives, widely used in biomedical applications. Other applications include adsorbent of metals and dyes from industrial wastes. Hydrogels based chitosan is used in drugs and proteins in pharmaceutical fields. This work mainly focuses on the polysaccharides such as, chitosan and its derivatives, whose chemical structure is modeled as a chemical graph and the data regarding edge and vertex partitioning are studied. In this work, using non-adjacent pairing of vertices approach, their polynomials are determined for various topological coindices for the polysaccharides chitosan and their chemical derivatives. These polynomials are termed CoM-polynomials, extension of M-polynomials for non-adjacent vertices. Topological coindices are the real numbers, representing the molecular structure of the chemical compound whose physicochemical characteristics can be studied that relates Quantitative Structure Property Relationship/Quantitative Structure Activity Relationship (QSPR/QSAR) investigations. CoMpolynomials are computed for the derivatives of chitosan such as alpha, beta and gamma chitin. CoM-polynomials of 11 degree-based topological coindices are determined and are compared for the derivatives of chitosan.

show abstract

“…Te most extensively researched compounds among the various zeolite structures are synthetic compounds and minerals with crystal structures resembling those of sodalite [5]. Various biochemical properties of sodalite and zeolite form constructions in terms of molecular descriptors are investigated in [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Structural Modelling and Characterization of Sodalite Material Network concerning the Irregularity Topological Indices

Zaman¹,

Salman²,

Ullah

et al. 2023

Journal of Mathematics

View full text Add to dashboard Cite

Topological characterization of 3D molecular structures is an emerging study area in theoretical and computational chemistry. These structural descriptors are used in a variety of domains, including chemical graph theory, drug delivery, and nanomaterial characterization. Quantitative structural descriptors can be used to characterize the chemical and physical properties of a given compound. Topological indices of molecular graphs are numerical quantities that allow us to collect information about the chemical structure and reveal its hidden qualities without performing experiments. Due to the low cost of implementation, zeolite networks are considered popular chemical networks. Zeolites are widely used networks with applications in chemistry, medicine, and commercial production owing to their excellent chemical features. The sodalite network is composed of a very unique type of zeolite framework called sodalite. It is a three-dimensional network of interconnected cages and tunnels that provide an ideal environment for a wide range of chemical and physical processes. This paper deals with the sodalite material network’s degree-based and reverse degree-based irregularity indices. These indices provide a quantitative measure of the irregular behaviour of the sodalite material network. It can be used to identify areas of the network where irregular behaviour is occurring and to compare different networks to determine which is more irregular. Additionally, these indices can be used to monitor changes in irregularity over time, allowing us to measure the impact of any interventions that are implemented.

show abstract

M-Polynomials and Associated Topological Indices of Sodalite Materials

Cited by 6 publications

References 46 publications

Applications of magnesium iodide structure via modified-polynomials

Applications of magnesium iodide structure via modified-polynomials

Comparative study of chitosan derivatives through CoM‐polynomial

Three-Dimensional Structural Modelling and Characterization of Sodalite Material Network concerning the Irregularity Topological Indices

Contact Info

Product

Resources

About