2024
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Browsing 2024 by Subject "05C09"
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Item A novel approach to determine the Sombor-type indices via M-polynomial(Springer Nature, 2024) Kumar V.; Das S.Topological indices can be interpreted as the mathematical characterizations of a molecular compound and are significantly employed to forecast its physical, chemical and biological information. Computation of topological indices of a graph through its associated graph polynomial is a modern and optimal approach. One such method is to determine the degree-based topological indices of a graph using its M-polynomial. Among the class of degree-based topological indices, the Sombor indices are one of the most investigated indices in recent times. In this article, the M-polynomial-based derivation formulas are derived to compute the different Sombor-type indices, namely the Sombor index, modified Sombor index, first and second Banhatti�Sombor indices, and their reduced form of the Sombor indices. Furthermore, our proposed derivation formulas are applied to compute the Sombor-type indices of the jagged-rectangle benzenoid system Bm,n. Additionally, the comparison among the Sombor-type indices of Bm,n is presented through numerical and graphical representations. � The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2024.Item Geometric-Quadratic and Quadratic-Geometric Indices-based Entropy Measures of Silicon Carbide Networks(Springer Science and Business Media B.V., 2024) Das S.; Kumar V.; Barman J.In chemical graph theory, topological indices are numerical quantities associated with the structure of molecular compounds. These indices are utilized in the construction of quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR) analysis and quantify the different features of the molecular topology. M-polynomial gives a handy method for managing complex computations involving various indices and offers a consistent methodology to derive multiple degree-based topological indices. Graph entropy measures are employed to measure the structural information content, disorder and complexity of a graph. In this article, we examine the geometric-quadratic (GQ) and quadratic-geometric (QG) indices for silicon carbide networks, namely Si2C3-I[p,q], Si2C3-II[p,q] and Si2C3-III[p,q] with the help of their respective M-polynomials. Next, we propose the idea of the GQ-QG indices-based entropy measure and compute their expressions for the above-said networks. Furthermore, the graphical representation and numerical computation of the GQ-QG indices and associated entropy measures are performed to assess their behavior. These indices and entropy measures may be helpful in predicting the physico-chemical properties and understanding the structural behavior of the considered silicon carbide networks. � The Author(s), under exclusive licence to Springer Nature B.V. 2024.Item On sufficient condition for t-toughness of a graph in terms of eccentricity-based indices(Springer, 2024) Kori R.; Prasad A.; Upadhyay A.K.Let ?(G) be the number of components of graph G. For t?0 we call G t-tough if t�?(G-X)?|X|, for every X?V(G) with ?(G-X)?2. 1-tough graphs are also called Hamiltonian graphs. The eccentric connectivity index of a connected graph G denoted by ?c(G), is defined as ?c(G)=?v?V(G)?(v)d(v). The eccentric distance sum of a connected graph G is denoted by ?d(G), is defined as ?d(G)=?v?V(G)?(v)D(v). The connective eccentricity index of a connected graph G denoted as ?ce(G), is defined as ?ce(G)=?v?V(G)d(v)?(v), where ?(v) is the eccentricity of the vertex v, D(v) is the sum of the distance from to all other vertices, and d(v) is the degree of vertex v. Finding sufficient conditions for a graph to possess certain properties is a meaningful and important problem. In this article, we give sufficient conditions for t-toughness graphs in terms of the eccentric connectivity index, eccentric distance sum, and connective eccentricity index. � The Author(s), under exclusive licence to The National Academy of Sciences, India 2024.Item On topological indices of Molnupiravir and its QSPR modelling with some other antiviral drugs to treat COVID-19 patients(Springer Science and Business Media Deutschland GmbH, 2024) Das S.; Rai S.; Kumar V.The global pandemic caused by the novel virus SARS-CoV-2 (Severe Acute Respiratory Syndrome CoronaVirus 2), also known as COVID-19, is now a serious public health concern that has affected people worldwide. The condition has become worse due to a lack of adequate treatment. To combat the pandemic, several drugs are being investigated. A topological index (or molecular descriptor) is a numerical parameter that correlates the molecular structure of a chemical compound to its various physico-chemical properties and plays a significant role in the development of QSPR/QSAR (quantitative structure�property relationship/quantitative structure-activity relationship) models. In this study, we evaluate the degree-based topological indices (namely, the Nirmala index, first and second inverse Nirmala indices, geometric-quadratic and quadratic-geometric indices) of nine antiviral drugs (namely, Molnupiravir, Remdesivir, Chloroquine, Ritonavir, Theaflavin, Arbidol, Hydroxychloroquine, Thalidomide and Lopinavir) used in the remedy of COVID-19 patients, with the help of their respective M-polynomials. Also, we calculate the neighborhood degree sum-based indices of Molnupiravir by using its neighborhood M-polynomial (that is, NM-polynomial). In addition, we execute the correlation analysis among the topological indices and physico-chemical properties of these antiviral drugs. Furthermore, we demonstrate the QSPR models for strong correlation through the linear, quadratic and cubic regression analysis to appraise the effectiveness of the topological indices. And, the squared correlation coefficients obtained from the performed curvilinear regression models are compared with those acquired in the previous studies. The obtained topological indices and established QSPR models which may be helpful to predict the pharmacokinetic properties of these antiviral drugs and in the discovery of new drugs related to the medication for the COVID-19 pandemic. � The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023.
