The thesis deals with topics from the field of chemical graph theory. The Hosoya index of a graph $G$ is defined as ${Z(G) = \sum_{k \geq 0} p(G,k)}$, where $p(G,k)$ is the number of $k$-matchings in the graph $G$, and is associated with many thermodynamic properties such as boiling point, entropy and total $\pi$-electron energy. The aim of this thesis is to present a way to compute the Hosoya index of catacondensed benzenoid systems with transfer matrix technique.
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