Edge Irregularity Strength: A Complementary Descriptor to Topological Indices in QSPR and QSAR Studies
U. Vijaya Chandra Kumar, H. M. Nagesh, Narahari N
TL;DR
The paper addresses augmenting conventional QSPR/QSAR descriptors with edge irregularity strength (EIS), a graph-labeling measure that encodes molecular irregularities in graph representations. It proves a lower bound $es(G) \geq \max\{ \lceil (|E(G)|+1)/2 \rceil, \Delta(G) \}$ and demonstrates computation on Naphthalene with $|E|=11$ and $\Delta=3$, giving $es(G)=6$. Across a benzenoid hydrocarbon dataset, EIS shows strong linear relationships with experimental properties, e.g., $Y = aX + b$ with $R^2$ values up to about $0.99$ for $E_\pi$, PO, and MR, and high $R^2$ for BP, MW, XLogP3, HAC, etc. A comparative analysis with previous work indicates somewhat weaker correlations but still strong, supporting EIS as a complementary descriptor to traditional topological indices in QSPR/QSAR. Computational complexity for exact es(G) on larger structures motivates future work toward faster calculation methods.
Abstract
In chemical graph theory, topological indices are widely used as numerical descriptors for establishing quantitative structure-property relationships (QSPR) and quantitative structure-activity relationships (QSAR). These indices successfully correlate molecular structure with various physicochemical and biological properties. In addition to these methods, the concept of edge irregularity strength, a graph labeling measure, offers another perspective for representing structural characteristics. In this context, the edge irregularity strength concept provides a systematic way of assigning numerical labels to atoms based on specific rules. In this work, we explore the chemical applicability of the edge irregularity strength and demonstrate that it can also serve as a predictive tool for physicochemical properties, similar to topological indices. The findings show that the edge irregularity strength captures molecular features and complements existing approaches to structure-property analysis in chemical graph theory.