| Title: | A method for computing the edge-Hosoya polynomial with application to phenylenes |
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| Authors: | ID Knor, Martin (Author)
ID Tratnik, Niko (Author) |
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| Files: |  PDF - Presentation file, download (530,53 KB)
MD5: C3CD3FE3F642081C3744FF6A89922310
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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. |
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| Keywords: | edge-Hosoya polynomial, graphs, phenylenes |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | str. 605-629 |
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| Numbering: | Vol. 89, no. 3 |
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| PID: | 20.500.12556/DiRROS-18448  |
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| UDC: | 519.17 |
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| ISSN on article: | 0340-6253 |
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| DOI: | 10.46793/match.89-3.605K |
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| COBISS.SI-ID: | 142041603 |
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| Publication date in DiRROS: | 18.03.2024 |
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| Views: | 632 |
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| Downloads: | 444 |
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