Malaysian Journal of Mathematical Sciences, March 2026, Vol. 20, No. 1
A Study of Extremal Trees for the $ABS$ Index Based on Total Domination Number and Its Predictive Power in Molecular Modeling
Manuel, M. and Parthiban A.
Corresponding Email: parthiban.a@vit.ac.in
Received date: 20 January 2025
Accepted date: 3 July 2025
Abstract:
The atom-bond sum-connectivity $(ABS)$ index is a refined topological descriptor derived from several well-known chemical graph indices, including the sum-connectivity index $(SCI)$, the atom-bond connectivity index $(ABC)$ and the Randić index $(R)$. In recent years, exploring the interplay between topological indices and graph parameters has become a prominent area of research. This paper establishes a new lower bound for the $ABS$ index of trees in terms of their total domination number. Extremal trees that achieve this bound are characterized, providing insight into structural configurations that optimize the index under domination constraints. To evaluate the practical applicability of the theoretical results, a set of carboxylic acid molecules is examined using linear regression models. The predictive power of the $ABS$ index in capturing key physicochemical properties is assessed and compared against its variants$-ABC$, $SCI$ and $R$ indices. The analysis reveals strong correlations between these indices and molecular properties, underscoring their effectiveness in chemical informatics. Overall, this work integrates graph theory and molecular chemistry, demonstrating the value of topological indices in understanding and modeling chemical behavior.
Keywords: atom-bond sum-connectivity index; total domination number; extremal trees; QSPR analysis.
