رضا شرف دینی

Let $G$ be a simple graph. A matching (or independent edge set) of $G$ is a set of edges of $G$ no two of which have common vertex. The Hosoya index of a graph $G$ is defined as the total number of its matchings. An independent vertex set of $G$ is a set of vertices of $G$ no two of which are adjacent. The Merrifield-Simmons index (or Fibonachi number) of $G$ is defined as the total number of the independent vertex sets of $G$. In this thesis we present explicit formulas for the Hosoya and Merrifield-Simmons indices of several classes of graphs, like bridge and splice graphs arising from simpler graphs.