PYTHON-BASED COMPUTATION OF NSo(G) ENERGY: BOUNDS AND QSPR ANALYSIS ON COVID-19 DRUGS
Sunilkumar M. Hosamani, Ravishankar L. Hutagi, Umesh S. Mujumdar
Department of Mathematics, Rani Channamma University, Belagavi – 591156, Karnataka, India
Abstract: In this paper, we introduce a novel variant of the Sombor matrix, denoted by NSo(G), for a simple graph G. This matrix is defined such that for vertices i≠j, the (i,j)-entry is given by √(d_i^2+d_j^2 ), where d_i represents the degree of the i^th vertex, and zero otherwise. Let η_1≥η_2≥⋯≥η_n denote the eigenvalues of NSo(G) with η_1 corresponding to the spectral radius, and let the associated Sombor energy E_NSo (G) be defined as the sum of the absolute values of these eigenvalues. We develop a Python-based computational framework to determine the spectrum and energy of NSo(G) and derive new upper and lower bounds for both η_1 and E_NSo (G) in terms of the first Zagreb index M_1 (G). As an application, we conduct a Quantitative Structure-Property Relationship (QSPR) analysis on a dataset comprising drugs used in the treatment of COVID-19, constructing linear regression models to explore the correlation between the physicochemical properties of these drugs and their corresponding E_NSo (G) values, with results illustrated through graphical representations.
Keywords: Sombor matrix, Sombor energy, spectral radius, COVID-19.