A method for computing the edge-Hosoya polynomial with application to phenylenesKnor, Martin (Avtor) Tratnik, Niko (Avtor) Tratnik, Niko (Korespondenčni avtor) edge-Hosoya polynomialgraphsphenylenesThe edge-Hosoya polynomial of a graph is the edge version of the famous Hosoya polynomial. Therefore, the edge-Hosoya polynomial counts the number of (unordered) pairs of edges at distance $k \ge 0$ in a given graph. It is well known that this polynomial is closely related to the edge-Wiener index and the edge-hyper-Wiener index. As the main result of this paper, we greatly generalize an earlier result by providing a method for calculating the edge-Hosoya polynomial of a graph $G$ which is obtained by identifying two edges of connected bipartite graphs $G_1$ and $G_2$. To show how the main theorem can be used, we apply it to phenylene chains. In particular, we present the recurrence relations and a linear time algorithm for calculating the edge-Hosoya polynomial of any phenylene chain. As a consequence, closed formula for the edge-Hosoya polynomial of linear phenylene chains is derived. University of Kragujevac20232024-03-20 07:52:57Članek v reviji87534UDK: 519.17COBISS_ID: 142041603DOI: 10.46793/match.89-3.605KISSN pri članku: 0340-6253sl