ISSN print edition: 0366-6352 ISSN electronic edition: 1336-9075 Registr. No.: MK SR 9/7 Published monthly

A graph theoretical and multicriteria decision framework for physicochemical evaluation of drugs used in cancer treatment via graph energy

Hasnain Hayat, Muhammad Kamran Siddiqui, and Sarfraz Ahmad

Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan

E-mail: hasnainhyat11@gmail.com

Received: 14 January 2026  Accepted: 12 March 2026

Abstract:

This work relies on graph theory and computational techniques to analyze drugs that combat cancer treatment using their molecular and physicochemical properties. A graph of each drug molecule is drawn and adjacency matrices of these graphs are used for the calculation of graph energy and different topological indices characterizing structural and electronic parameters. Regression analysis for relating molecular descriptors with physicochemical properties provides quantitative information regarding the behavior of the drugs. Further, MCDM techniques such as TOPSIS and SAW have been utilized to establish rank for the drugs considering combined structural, chemical, and pharmacological parameters. This procedure provides a comprehensive framework for drug evaluation and it presents the role of graph-theoretical descriptors within drug design and offers a valid ranking of gastric cancer therapeutics for informed decisions.

Graphical abstract

The proposed framework transforms gastric cancer drug molecules into molecular graphs from which adjacency matrices, graph energy, and degree-based topological indices are computed to characterize structural and electronic features. These graph-theoretical descriptors are combined with physicochemical properties to form a unified decision matrix, which is analyzed using multicriteria decision-making techniques, including TOPSIS and the Simple Additive Weighting method. This integrated workflow enables a systematic evaluation and ranking of gastric cancer drugs by simultaneously considering molecular structure, physicochemical behavior, and quantitative decision metrics, providing a transparent and mathematically grounded tool for drug assessment.

The structure of daunorubicin

Keywords: Graph theory; Graph energy-based indices; Drugs used in cancer treatment; Physicochemical characteristics; Regression modeling; Multi criteria decision making (MCDM) techniques; Drug ranking

Full paper is available at www.springerlink.com.

DOI: 10.1007/s11696-026-04808-3

Chemical Papers 80 (6) 6947–6971 (2026)