فهرست نشریات علمی دسترسی آزاد ایران

‎Our main interest in this paper is the study of the Hosoya index $Z\left(G;\varphi \right) $ of weighted graphs $\left( G;\varphi \right) $‎, ‎when $G$ is a hexagonal chain with weight function induced by a vertex-degree-based topological index $\varphi$‎. ‎Recall that a hexagonal chain is a special type of hexagonal systems‎, ‎natural graph representations of benzenoid hydrocarbons‎. ‎On the other hand‎, ‎vertex-degree based topological indices are (molecular) graph descriptors which play a significant role in chemical graph theory‎.‎Concretely‎, ‎if $G$ is a hexagonal chain and $\varphi$ is a vertex-degree-based topological index‎, ‎we give a method to compute $Z\left(G;\varphi \right) $ in terms of products of namely four types of $4\times 4$ matrices associated to $\varphi$‎. ‎As a consequence‎, ‎under certain conditions on $\varphi$‎, ‎we show that the $\varphi$-weighted linear hexagonal chain attains the minimal value of the Hosoya index‎, ‎among all $\varphi$-weighted hexagonal chains‎.