On computation of newly defined degree-based topological invariants of Bismuth Tri-iodide via M-polynomial

Hameed, Saira; Husin, Mohamad Nazri; Afzal, Farkhanda; Hussain, Hina; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat

doi:10.1080/09720529.2021.1972615

Cited by 23 publications

(4 citation statements)

References 28 publications

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“…Due to various uses in quantitative structure-activity and quantitative structure property relationships (QSPR), topological indices, which are structural invariants based on molecular graphs have attracted attention recent times. The indices based on degree have enormous applications in structural chemistry and is very important, [14,15,25,13]. Such index measures are shown to be more efficient when combined with entropy and have found use in several őelds of research, including chemistry, biological systems, engineering, mathematics, physics, and Quantitative Structure ActivityRelationships (QSAR) etc [2], [16], [23], [24].…”

Section: Introductionmentioning

confidence: 99%

Various topological descriptors and corresponding Entropies of Iridium cored Dendrimer

Xavier

Ismail

Almusawa

et al. 2023

Preprint

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Measures of graph entropy have been widely used in information theory, biology, chemistry, and sociology, among other disciplines. The entropy of a probability distribution may be thought of as both an indicator of information and an indicator of uncertainty, and it is a number used in information theory to gauge the complexity of a graph. Mathematical and medicinal chemistry, including drug design, have previously made extensive use of information-theoretic network complexity measurements. Dendrimers belong to the world of molecular chemistry for stepwise controlled synthesis and to the world of polymers for repeating structures from monomers. A topological index is a numerical metric that describes the topology of a graph. Consequently , a topological index calculated for a molecular network is a quantitative indicator of molecular topology. Due to the simplicity of production and the speed at which these computations may be performed, these descriptors have gained great prominence in recent years. Characterizing molecular structure using topological methods, including numerical graph invariants, is a current trend in mathematics and computational chemistry. Such conceptual descriptors have also launched a broad range of applications in QSAR/QSPR investigations and is ideal for innovative molecular design, drug development, and risk assessment of chemicals. In this paper, various entropy measures along with the distance and degree based topological indices of highly efficient iridium cored electrophosphorescent dendrimer has been evaluated. Entropy measure is a topological feature that may be used to assess the complexity of chemical compounds.

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Section: Introductionmentioning

confidence: 99%

Various topological descriptors and corresponding Entropies of Iridium cored Dendrimer

Xavier

Ismail

Almusawa

et al. 2023

Preprint

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“…Fruitful results of such newly defined degree based topological invariants of the M-polynomial, tadepol graph are discussed in [22] and [23]. Computation of entropy measures and valency-based indices of networks are discussed in [24] and [25].…”

Section: Introductionmentioning

confidence: 99%

Properties of Graph Based on Divisor-Euler Functions

Rehman,

Mehmood

2023

Sci Inquiry Rev.

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Divisor function gives the residues of which divide it. A function denoted by counts the total possible divisors of and gives the list of co-prime integers to . Many graphs had been constructed over these arithmetic functions. Using and , a well known graph named as divisor Euler function graph has been constructed. In this paper, we use divisor function and anti Euler function . We label the symbol to count those residues of which are not co-prime to . By using these functions, we find a new graph, called divisor anti-Euler function graph (DAEFG), denoted as . Let be a DAEFG, where and . The objective of this sequel is to introduce and discuss the properties of DAEFG. In this work, we discuss novel classes of proposed graph with its structure using loops, cycles, components of graph, degree of its vertices, components as complete, bipartite, planar, Hamiltonian and Eulerian graphs. Also, we find chromatic number, chromatic index and clique of these graphs.

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“…Moreover, revan indices and revan polynomials of silicon carbide graphs were investigated in [19]. The authors determined the novel degree-based topological characteristics of bismuth tri-iodide, using the M-polynomial in [20]. Kosari et al [21] formulated an optimal lower limit for the KG-Sombor index of trees, considering both their order and maximum degree.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Various Topological Indices of Flabellum Graphs

Shi,

Kosari,

Ahmad

et al. 2023

Mathematics

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Graph theory serves as an engaging arena for the investigation of proof methods within the field of discrete mathematics, and its findings find practical utility in numerous scientific domains. Chemical graph theory is a specialized branch of mathematics that uses graphs to represent and analyze the structure and properties of chemical compounds. Topological indices are mathematical properties of graphs that play a crucial role in chemistry. They provide a unique way to connect the structural characteristics of chemical compounds to their corresponding molecular graphs. The flabellum graph Fn(k,j) is obtained with the help of k≥2 duplicates of the cycle graph Cn with a common vertex (known as, central vertex). Then, in j of these duplicates, additional edges are added, joining the central vertex to all non-adjacent vertices. In this article, we compute different degree-based topological indices for flabellum graphs, including some well known indices, such as the Randić index, the atom bond connectivity index, the geometric–arithmetic index, and the Zagreb indices. This research provides an in-depth examination of these specific indices within the context of flabellum graphs. Moreover, the behavior of these indices is shown graphically, in terms of the parameters j,k, and n. Additionally, we have extended the concept of the first Zagreb index, to address the issue of cybercrime. This application enables us to identify criminals who exhibit higher levels of activity and engagement in multiple criminal activities when compared to their counterparts. Furthermore, we conducted a comprehensive comparative analysis of the first Zagreb index against the closeness centrality measure. This analysis sheds light on the effectiveness and relevance of the topological index in the context of cybercrime detection and network analysis.

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On computation of newly defined degree-based topological invariants of Bismuth Tri-iodide via M-polynomial

Cited by 23 publications

References 28 publications

Various topological descriptors and corresponding Entropies of Iridium cored Dendrimer

Various topological descriptors and corresponding Entropies of Iridium cored Dendrimer

Properties of Graph Based on Divisor-Euler Functions

Evaluation of Various Topological Indices of Flabellum Graphs

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