M-polynomial and neighborhood M-polynomial methods for topological indices of porous graphene

Shanmukha, M. C.; Usha, A.; Shilpa, K; Basavarajappa, N.S.

doi:10.1140/epjp/s13360-021-02074-8

Cited by 28 publications

(14 citation statements)

References 31 publications

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“…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%

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Comparative study of chitosan derivatives through CoM‐polynomial

Shanmukha¹,

Usha

2022

Int J of Quantum Chemistry

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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.

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“…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%

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

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“…Namely, computations can be translated to elementary calculus, see [5,6]. The list of papers [1][2][3][14][15][16][17] is only a small part of the research in which the M-polynomial is a key tool used. A general approach to degree-based topological indices has been done in [10], while in [8] investigations of their structure-sensitivity in chemistry was performed.…”

Section: Introductionmentioning

confidence: 99%

How to Compute the M-Polynomial of (Chemical) Graphs

Deutsch¹,

Klavžar²,

Romih³

2022

MATCH

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Let G be a graph and let mi,j(G), i, j ≥ 1, be the number of edges uv of G such that {dv(G), du(G)} = {i, j}. The M-polynomial of G is M (G; x, y) = i≤j mi,j(G)x i y j . A general method for calculating the M-polynomials for arbitrary graph families is presented. The method is further developed for the case where the vertices of a graph have degrees 2 and p, where p ≥ 3, and further for such planar graphs. The method is illustrated on families of chemical graphs.

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“…Topological index(TI's) is important in chemical graph theory since it provides scientists with a wealth of information relating to the construction of chemical compounds. The TI's is an arithmetical characteristic features that describes the network topology of molecule's structure and makes numerous predictions about molecular characteristics [1,2].…”

Section: Introductionmentioning

confidence: 99%

Results on certain biopolymers using M-polynomial and NM-polynomial of topological indices

Yasin

Suresh

2022

Preprint

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The topological indices is a numerical descriptors that helps in forecasting the physio-chemical characteristics and biological actions of a chemical molecules. It is often helpful forecast numerous physiochemical attributes and biological actions of molecules in chemometrices, bioinformatics and biomedicines. In the present work establish the M-polynommial and NM-polynomial of some utmost familiar biopolymers (xanthan gum, gellan gum and polyacrylamide). These polynomials are used to extract certain degree-based TI’s. The uses of these biopolymers, which can increasingly take the place of traditional admixtures for the application of soil stability and enhancement. Mathematics Subject Classification 05C92 . 05C09 . 92E10

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M-polynomial and neighborhood M-polynomial methods for topological indices of porous graphene

Cited by 28 publications

References 31 publications

Comparative study of chitosan derivatives through CoM‐polynomial

Comparative study of chitosan derivatives through CoM‐polynomial

How to Compute the M-Polynomial of (Chemical) Graphs

Results on certain biopolymers using M-polynomial and NM-polynomial of topological indices

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