Double gaussianization of graph spectra

Tools

Alhomaidhi, Alhanouf and Al-Thukair, Fawzi and Estrada, Ernesto (2021) Double gaussianization of graph spectra. Applied Mathematical Modelling, 93. pp. 134-147. ISSN 0307-904X (https://doi.org/10.1016/j.apm.2020.12.018)

[thumbnail of Alhomaidhi-etal-AMM-2021-Double-gaussianization-of-graph]
Preview
 Text. Filename: Alhomaidhi_etal_AMM_2021_Double_gaussianization_of_graph.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo
Download (1MB)| Preview

Abstract

The graph spectrum is the set of eigenvalues of a simple graph with n vertices. Here we fold this graph spectrum at a given pair of reference eigenvalues and then exponentiate the resulting folded graph spectrum. This process produces double Gaussianized functions of the graph adjacency matrix which give more importance to the reference eigenvalues than to the rest of the spectrum. Based on evidences from mathematical chemistry we focus here our attention on the reference eigenvalues ±1. In the examples that we have examined, they enclose most of the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of organic molecular graphs. We prove here several results for the trace of the double Gaussianized adjacency matrix of simple graphs–the double Gaussianized Estrada index. Finally we apply this index to the classification of polycyclic aromatic hydrocarbons (PAHs) as carcinogenic or inactive ones. We discover that local indices based on the previously developed matrix function allow to classify correctly 100% of the PAHs analyzed. Such indices reflect the electron population of the HOMO/LUMO and eigenvalues close to them, in the so-called K and L regions of PAHs.

ORCID iDs

Alhomaidhi, Alhanouf ORCID logoORCID: https://orcid.org/0000-0003-0762-5807, Al-Thukair, Fawzi and Estrada, Ernesto;
  • Item type:Article
    ID code:77249
    Dates:
    Date
    Event
    31 May 2021
    Published
    30 December 2020
    Published Online
    13 December 2020
    Accepted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:30 Jul 2021 16:02
    Last modified:23 Nov 2024 01:16
    URI:https://strathprints.strath.ac.uk/id/eprint/77249
CORE (COnnecting REpositories)