Some stable and closed-shell structures of anticancer drugs by graph theoretical parameters

Ali N A Koam; Ali Ahmad; Muhammad Azeem; Khalil Hadi Hakami; Kashif Elahi

doi:10.1016/j.heliyon.2023.e17122

Some stable and closed-shell structures of anticancer drugs by graph theoretical parameters

Heliyon. 2023 Jun 14;9(6):e17122. doi: 10.1016/j.heliyon.2023.e17122. eCollection 2023 Jun.

Authors

Ali N A Koam¹, Ali Ahmad², Muhammad Azeem³, Khalil Hadi Hakami¹, Kashif Elahi⁴

Affiliations

¹ Department of Mathematics, College of Science, Jazan University, New Campus, Jazan 2097, Saudi Arabia.
² Department of Information Technology and Security, College of Computer Science and Information Technology, Jazan University, Saudi Arabia.
³ Department of Mathematics, Riphah International University Lahore, Pakistan.
⁴ Deanship of E-learning and Information Technology, Jazan University, Jazan, Saudi Arabia.

Abstract

The eigenvalues are significant in mathematics, but they are also relevant in other domains like as chemistry, economics, and a variety of others. In terms of our research, eigenvalues are used in chemistry to represent not only the form of energy but also the various physicochemical aspects of a chemical substance. We must comprehend the connection between mathematics and chemistry. The antibonding level is related to positive eigenvalues, the bonding level is associated to negative eigenvalues, and the nonbonding level is linked to zero eigenvalues. In this work, we studied some anticancer drug structures in terms of nullity, matching number, eigenvalues of adjacency matrix, and characteristics polynomials. As a result, Carmustine, Caulibugulone-E, Aspidostomide-E anticancer drug structures are stable, closed-shell molecules since their nullity is equal to zero.

Keywords: 05C10; 05C50; 05C70; 05C90; 15A18; 15A90; 74E40; 74F25; Anticancer drugs; Characteristics polynomials; Cyclomatic number; Eigenvalues; Energy; First Betti number; Inertia; Matching number; Nullity.