Chemistry as the science of the properties and behavior of matter composed of molecules, or molecular substances. Since the latter consists of atoms and the bonding patterns between them, chemistry is naturally linked to the graph theory that maps structure to the corresponding graph(s). Especially, within the known theory of Bader of ‘Atoms-in-Molecules’. One can say that “chemical graph theory is an emerging subfield of mathematical chemistry which helps in providing us tools such as polynomials and functions [G. Rucker and C. Rucker, “On topological indices, boiling points, and cycloalkanes”, J. Chem. Inf. Comput. Sci. 39, 788–802 (1999)] to characterize properties of substances [S. Klavzar and I. Gutman, “A comparison of the Schultz molecular topological index with the Wiener index”, ibid. 36, 1001–1003 (1996)]” – these words enter the paper under review. The present reviewer himself was also fascinated, as PhD student, by this connection that some of his first works were dedicated to developing the graph theory to the structure of many-electron reduced density matrices [G. G. Daydyusha and E. S. Kryachko, “Algebraic structure of fermion density matrices. I and II”, Intern. J. Quantum Chem. 19, 251–257, 505–514 (1981)].
Let us return to the present paper under review. It actually examines the application of the chemical graph theory to study topological indices and aims to establish closed formulas for M-polynomials of linear chains of benzene, naphthalene, and anthracene graphs. In this paper, the authors also compute some topological indices related to these graphs: first and second Zagreb indices, modified second Zagreb index, generalized and inverse Randić indices, symmetric division index, harmonic index, inverse Sum index, and augmented Zagreb index. These results will be useful in pharmacy, drug design, and many other applied fields of molecular sciences.