# Novel Roman domination-based graph energies for QSPR analysis of neuroprotective herbal compounds in Alzheimer’s disease treatment

## TL;DR

This paper introduces a new graph-based method for analyzing herbal compounds that may help treat Alzheimer's disease, showing better accuracy than traditional methods.

## Contribution

The paper introduces novel Roman domination-based graph energies for QSPR analysis of herbal compounds.

## Key findings

- Roman domination-based graph energies outperformed classical approaches in QSPR modeling.
- Quadratic regression showed the strongest correlations and lowest standard error.
- Validation on Kaempferol demonstrated high predictive reliability (r=0.993).

## Abstract

Alzheimer’s disease (AD) is a progressive neurodegenerative disorder for which U.S. Food and Drug Administration (FDA)-approved drugs provide only temporary symptomatic relief and often cause adverse effects. Plant-derived bioactive phytochemicals are emerging as promising alternatives due to their multi-targeted neuroprotective properties and reduced toxicity. In this article, herbal anti-Alzheimer’s compounds are analyzed using a novel graph molecular modeling. In chemical graph theory, molecular structures are represented as isomorphic molecular graphs
GV,E
, where
V
and
E
denote the set of vertices (atoms) and edges (chemical bonds) respectively. Classical graph matrices such as adjacency and Laplacian matrices capture the molecular connectivity but fail to account for hierarchical differences in atomic influence. To address this limitation, Roman domination is employed to represent the hierarchical dominance of atoms within molecular structures. A Roman domination function (RDF) on a graph
GV,E
is a mapping
f:V→0,1,2
such that every atom
v
with
fv=0
has at least one adjacent atom
u
with
fu=2
, reflecting the hierarchical dominance within the isomorphic molecular graph. Based on this principle, the Roman domination-based matrices and corresponding graph energies are introduced in this article. Quantitative Structure-Property Relationship (QSPR) graph models are developed using the Roman energies through linear, quadratic and cubic regression analysis. The results demonstrate superior performance compared to classical approaches, with the quadratic regression showing the strongest correlations and lowest standard error. Internal validation through the Y-randomization and Leave-One-Out Cross-Validation methods confirmed the stability of the models, while external validation on the herbal compound Kaempferol (
r=0.993
) further supported their predictive reliability. These findings underscore the robustness of Roman energies, establishing them as powerful molecular descriptors that offer enhanced accuracy in the QSPR analysis and hold promise for applications in drug design, materials informatics and computational chemistry.