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  • A method for computing the edge-Hosoya polynomial with application to phenylenes
    Knor, Martin ; Tratnik, Niko
    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.
    Source: Match : communications in mathematical and in computer chemistry. - ISSN 0340-6253 (Vol. 89, no. 3, 2023, str. 605-629)
    Type of material - article, component part ; adult, serious
    Publish date - 2023
    Language - english
    COBISS.SI-ID - 142041603

    Link(s):

    DiRROS - Digital repository of Slovenian research organizations
    Digital Library of the University of Maribor – DLUM

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