On Neighborhood Inverse Sum Indeg Energy of Molecular Graphs

Abstract

The spectral graph theory explores connections between combinatorial features of graphs and algebraic properties of associated matrices. The neighborhood inverse sum indeg (NI) index was recently proposed and explored to be a significant molecular descriptor. Our aim is to investigate the NI index from a spectral standpoint, for which a suitable matrix is proposed. The matrix is symmetric since it is generated from the edge connection information of undirected graphs. A novel graph energy is introduced based on the eigenvalues of that matrix. The usefulness of the energy as a molecular structural descriptor is analyzed by investigating predictive potential and isomer discrimination ability. Fundamental mathematical properties of the present spectrum and energy are investigated. The spectrum of the bipartite class of graphs is identified to be symmetric about the origin of the real line. Bounds of the spectral radius and the energy are explained by identifying the respective extremal graphs.

Graph Energy Variants and Topological Indices in Platinum Anticancer Drug Design: Mathematical Insights and Computational Analysis with DFT and QTAIM

“…Notably, we have observed that the energy associated with most degree-based topological indices exhibits a higher correlation coefcient than calculation-based topological indices and is more signifcant. Compared to the literature [46,47], where the topological indices have a higher correlation coefcient, our results are more interesting. Furthermore, our study has mathematically determined the upper and lower bounds of the topological indices, enabling their application to any chemical structure.…”

“…However, it appears that most of these novel energies have been introduced without considering their specifc utility in chemistry or other relevant felds. Tis study, in contrast, follows a more deliberate approach, drawing inspiration from a previous study [46] that introduces a suitably constructed matrix to generate a novel graph energy based on the eigenvalues of the neighborhood inverse (NI) sum index. Te NI index demonstrates predictive potential and can efectively discriminate between isomers, making it a valuable molecular structural descriptor.…”

Expected values of sum-based topological indices of random cyclodecane chains

“…For results related to neighborhood sum-degree-based indices, refer to [17,[20][21][22][23][24][25].…”

The study of pentagonal chain with respect to schultz index, modified schultz index, schultz polynomial and modified schultz polynomial

“…The Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs are obtained in [38]. Recently, Ullah et al, obtained some interesting results on structural characterizations of graphs through degree based topological indices [39][40][41][42][43] and Mondal et al, studied the molecular graphs in [44][45][46][47]. On the other hand, some other properties of topological indices are discussed by Ahmad et al, [48][49][50][51] and Zaman et al, in [52][53][54][55][56][57][58][59].…”