TY - JOUR

T1 - On topological polynomials and indices for metal-organic and cuboctahedral bimetallic networks

AU - Yasmeen, Farhana

AU - Imran, Muhammad

AU - Akhter, Shehnaz

AU - Ali, Yasir

AU - Ali, Kashif

N1 - Funding Information:
Funding information: This research is supported by the UPAR Grant of United Arab Emirates University (UAEU), Al Ain, United Arab Emirates via Grant No. G00002590 and UPAR Grant of UAEU via Grant No. G00003271.
Publisher Copyright:
© 2022 Farhana Yasmeen et al., published by De Gruyter.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - A molecular graph consists of bonds and atoms, where atoms are present as vertices and bonds are present as edges. We can look at topological invariants and topological polynomials that furnish bioactivity and physio-chemical features for such molecular graphs. These topological invariants, which are usually known as graph invariants, are numerical quantities that relate to the topology of a molecular graph. Let mpq(X) be the number of edges in X such that (ζa, ζb) = (p, q), where ζa (or ζb) present the degree of a (or b). The M-polynomial for X can be determined with the help of relation M(X;x, y) = ∑p≤ qmpq(X)xpyq. In this study, we calculate the M-polynomial, forgotten polynomial, sigma polynomial and Sombor polynomial, and different topological invariants of critical importance, referred to as first, second, modified and augmented Zagreb, inverse and general Randić, harmonic, symmetric division; forgotten and inverse invariants of chemical structures namely metal-organic networks (transition metal-tetra cyano benzene organic network) and cuboctahedral bimetallic networks (MOPs) are retrieved using a generic topological polynomial approach. We also draw the two-dimensional graphical representation of outcomes that express the relationship between topological indices and polynomial structural parameters.

AB - A molecular graph consists of bonds and atoms, where atoms are present as vertices and bonds are present as edges. We can look at topological invariants and topological polynomials that furnish bioactivity and physio-chemical features for such molecular graphs. These topological invariants, which are usually known as graph invariants, are numerical quantities that relate to the topology of a molecular graph. Let mpq(X) be the number of edges in X such that (ζa, ζb) = (p, q), where ζa (or ζb) present the degree of a (or b). The M-polynomial for X can be determined with the help of relation M(X;x, y) = ∑p≤ qmpq(X)xpyq. In this study, we calculate the M-polynomial, forgotten polynomial, sigma polynomial and Sombor polynomial, and different topological invariants of critical importance, referred to as first, second, modified and augmented Zagreb, inverse and general Randić, harmonic, symmetric division; forgotten and inverse invariants of chemical structures namely metal-organic networks (transition metal-tetra cyano benzene organic network) and cuboctahedral bimetallic networks (MOPs) are retrieved using a generic topological polynomial approach. We also draw the two-dimensional graphical representation of outcomes that express the relationship between topological indices and polynomial structural parameters.

KW - Cuboctahedral bimetallic

KW - M-polynomial

KW - Metal-organic networks

KW - Sigma polynomial

KW - Sombor polynomial

KW - Topological indices

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U2 - 10.1515/mgmc-2022-0012

DO - 10.1515/mgmc-2022-0012

M3 - Article

AN - SCOPUS:85137655470

SN - 0792-1241

VL - 45

SP - 136

EP - 151

JO - Reviews on silicon, germanium, tin and lead compounds

JF - Reviews on silicon, germanium, tin and lead compounds

IS - 1

ER -