A Study on Partition-Based Resolving Parameters in Molecular Graphs of Anticancer Drugs

Abstract

Cancer remains one of the most life-threatening diseases worldwide, and effective therapeuticoptions are still limited for several cancer types. Recently, HDAC-based multitarget anti-cancer drugs have attracted considerable attention due to their promising biological activity. Inchemical graph theory, drug molecules are often represented using graph models, where atomscorrespond to vertices and the chemical bonds between them are depicted as edges. One important graph invariant is the partition dimension, which measures the minimum number ofvertex partitions required to uniquely determine the position of every vertex in a graph basedon distance representations. In this paper, we investigate the partition dimension of moleculargraphs corresponding to the anticancer drugs vorinostat, tucidinostat, triciferol, CUDC-101,and CUDC-907. These drugs play a significant role in modern cancer therapy, particularly inepigenetic and multitarget treatments. In the current study we build chemical graph modelsof the compounds under study, solve appropriate resolving partitions, and give accurate valueor bounds of these partition dimensions. The results show that partition dimension providesan effective and sparse structure of distinctly identifying atomic locations in complicated drugmolecules, thus highlighting its applicability as a potent structural label of anticancer moleculesand enhancing the interdisciplinary discussion between graph theory and medicinal chemistry.