Geodesic
The Hosoya polynomial of double weighted graphs
Ars Mathematica Contemporanea, Tome 15 (2018) no. 2, pp. 441-466.

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The modified Hosoya polynomial of double weighted graphs, i.e. edge and vertex weighted graphs, is introduced that enables derivation of closed expressions for Hosoya polynomial of some special graphs including unicyclic graphs. Furthermore, the Hosoya polynomial is given as a sum of edge contributions generalizing well known analogous results for the Wiener number. A linear algorithm for computing the Hosoya polynomial on cactus graphs is provided. Hosoya polynomial is extensively studied in chemical graph theory, and in particular its weighted versions have interesting applications in theory of communication networks.
DOI : 10.26493/1855-3974.1297.c7c
Keywords: Wiener number, Hosoya polynomial, Wiener polynomial, edge contributions, communication network, cactus graph, linear algorithm 
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Tina Novak; Darja Rupnik Poklukar; Janez Žerovnik. The Hosoya polynomial of double weighted graphs. Ars Mathematica Contemporanea, Tome 15 (2018) no. 2, pp. 441-466. doi : 10.26493/1855-3974.1297.c7c. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1297.c7c/

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