2024

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On sufficient condition for t-toughness of a graph in terms of eccentricity-based indices
(Springer, 2024) Rajkaran Kori; Abhyendra Prasad; Ashish K. Upadhyay
Let ω(G) be the number of components of graph G. For t⩾0 we call G t-tough if t·ω(G-X)⩽|X|, for every X⊆V(G) with ω(G-X)⩾2. 1-tough graphs are also called Hamiltonian graphs. The eccentric connectivity index of a connected graph G denoted by ξc(G), is defined as ξc(G)=∑v∈V(G)ϵ(v)d(v). The eccentric distance sum of a connected graph G is denoted by ξd(G), is defined as ξd(G)=∑v∈V(G)ϵ(v)D(v). The connective eccentricity index of a connected graph G denoted as ξce(G), is defined as ξce(G)=∑v∈V(G)d(v)ϵ(v), where ϵ(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.
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) Shibsankar Das; Shikha Rai; Virendra Kumar
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.