Analysis of the Hosoya and the Merrifield-Simmons indices on molecular structures

In this thesis, the focus is on the computation of the Hosoya index and Merrifield-Simmons index, which have significant applications in the field of chemical graph theory, by working on benzenoid systems in general. For ∀𝑘 ≥ 0 of each given cata-condensed benzenoid system, two different methods are presented, each based on the product of square matrices with natural numbers and a vector, used to compute the 𝑘-matching number and 𝑘-independence number, and for applicability of the methods, codes are written in MATLAB. As the main part of the study, a method that computes the Merrifield-Simmons index of each given cata-condensed benzenoid system by means of an appropriate product of matrices with natural numbers and a vector is proposed. Afterward, two different methods are proposed for the computation of the Hosoya and the Merrifield-Simmons indices specific to double benzenoid chains, which are a type of peri-condensed benzenoid chains, each of which is used to compute the relevant index. Finally, the computation of both the Hosoya and the Merrifield-Simmons indices for two special types of peri-condensed benzenoid systems represented by 𝑅𝑛 ve 𝑷𝒏 is presented as an explicit function expressed as the product of a power of a matrix and a vector.