20.500.12556/DKUM-87534 A method for computing the edge-Hosoya polynomial with application to phenylenes The 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. edge-Hosoya polynomial graphs phenylenes true true true University of Kragujevac Angleški jezik Slovenski jezik Članek v reviji 2024-03-20 07:52:57 2024-04-15 12:49:03 2024-04-16 10:23:05 0000-00-00 00:00:00 2023 0 0 str. 605-629 ǂno. ǂ3 ǂVol. ǂ89 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 2022-08-31 0000-00-00 519.17 142041603 10.46793/match.89-3.605K 0340-6253 http://dx.doi.org/10.46793/match.89-3.605K 1 7c07b3ea-e686-11ee-9087-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=177112 RAZ_Knor_Martin_2023.pdf RAZ_Knor_Martin_2023.pdf 1 2278BEC23BA16128AD7FC1659D4FAA07 e21981d1187646ccad9615b07f46facbd15b17385872af77dbdaf22a73af6dc6 a8220a1b-fb15-11ee-8f8b-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=178559 Fakulteta za naravoslovje in matematiko 0 0 0