Graph entropies, enumeration of circuits, walks and topological properties of three classes of isoreticular metal organic frameworks

Abraham, Jessie; Arockiaraj, Micheal; Jency, J. Martina; Kavitha, S.; Balasubramanian, K.

doi:10.1007/s10910-021-01321-8

Cited by 34 publications

(13 citation statements)

References 71 publications

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“…To implement Shannon’s entropy approach, we define the structural information function f on the edge set of MOF into a non-negative real number, and in our study, the structural information is taken as the bond measure induced from degree/degree-sum parameters. The entropy of MOF structures with structural information f is defined below, assuming that E (MOF) = { a 1 , a 2 , ..., a n }. As discussed in a series of papers, ,,, we replace the multiplicative component of the above equation with scalar multiplicative, and we arrive at the modified form of entropy as given below. …”

Section: Methodsmentioning

confidence: 99%

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Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks

Raza

Arockiaraj²,

Maaran³

et al. 2023

ACS Omega

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Metal organic frameworks (MOFs) are topical crystalline materials with high porosity and inner surface areas synthesized from naturally occurring minerals. Such MOFs with transition metals have attracted considerable attention because of their fascinating morphological diversity and tunable characteristics. The coronene-based structural frameworks with transition metal atoms are synthesized by repeating a fixed coronene unit at several levels. In this study, topological indices and NMR and ESR spectral patterns are computed for these MOFs to shed light on their structures and spectral properties. We obtained mathematical expressions of topological indices based on degree and degree-sum values of MOFs for the rectangular, hexagonal, and parallelogram peripheral shapes. Furthermore, the entropy measures of these novel frameworks are evaluated with the help of index functionals and compared to a wide range of degree-based descriptors. The NMR and ESR spectral patterns have been obtained from the distance degree vector sequences and symmetries for the three MOFs.

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Section: Methodsmentioning

confidence: 99%

“…As discussed in a series of papers, 28,30,45,46 we replace the multiplicative component of the above equation with scalar multiplicative, and we arrive at the modified form of entropy as given below.…”

Section: Methodsmentioning

confidence: 99%

Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks

Raza

Arockiaraj²,

Maaran³

et al. 2023

ACS Omega

Self Cite

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“…The concept of graph entropy or entropy of graph was first time appeared in [41], where molecular graphs are used to study the information content of an organism. Entropy-based methods are powerful tools to investigate various problems in cybernetics, mathematical chemistry, pattern recognition, and computational physics [22,39,42,43,44]. Third version of Zagreb index [28]:…”

Section: Introductionmentioning

confidence: 99%

Computational analysis of NM-polynomial based topological indices and graph-entropies of carbon nanotube Y-junctions

Lal¹,

Bhat²,

Sharma³

2023

Preprint

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Carbon nanotube Y-junctions are of great interest to the next generation of innovative multi-terminal nanodevices. Topological indices are graph-theoretically based parameters that describe various structural properties of a chemical molecule. The entropy of a graph is a topological descriptor that serves to characterize the complexity of the underlying molecular graph. The concept of entropy is a physical property of a thermodynamic system. Graph entropies are the essential thermophysical quantities defined for various graph invariants and are applied to measure the heterogeneity and relative stabilities of molecules. In this paper, several neighborhood degree sum-based topological indices including graph-based entropies of carbon nanotube Y-junction graphs are computed.

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“…Moreover, Yang et al [19] computed the vertex Szeged index of the structure of cubic crystals. Furthermore, Arockiaraj et al [20] and Abraham et al [21] explored the topological properties of other types of three-dimensional structures. Recently, Ali and Trinajstić [22] initiated a novel conception of connection number (CN) which is the cardinality of those nodes having length two from a certain vertex.…”

Section: Introductionmentioning

confidence: 99%

Topological Aspects of Molecular Networks: Crystal Cubic Carbons

Javaid

Sattar

Bonyah³

2022

Complexity

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Theory of networks serves as a mathematical foundation for the construction and modeling of chemical structures and complicated networks. In particular, chemical networking theory has a wide range of utilizations in the study of chemical structures, where examination and manipulation of chemical structural information are made feasible by utilizing the numerical graph invariants. A network invariant or a topological index (TI) is a numerical measure of a chemical compound which is capable to describe the chemical structural properties such as melting point, freezing point, density, pressure, tension, and temperature of chemical compounds. Wiener initiated the first distance-based TI which is considered to be the most important TI to preserve the chemical and physical properties of chemical structures. Later on, degree-based TI was introduced to find the π -electron energy of molecules. Recently, connection number-based TIs are studied which are more efficient than degree and distance-based TIs. In this paper, we compute the connection number-based TIs of the structure of crystal cubic carbons which are one of the most significant and interesting composites in modern resources of science due to the involvement of carbon atoms.

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Graph entropies, enumeration of circuits, walks and topological properties of three classes of isoreticular metal organic frameworks

Cited by 34 publications

References 71 publications

Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks

Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks

Computational analysis of NM-polynomial based topological indices and graph-entropies of carbon nanotube Y-junctions

Topological Aspects of Molecular Networks: Crystal Cubic Carbons

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