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Journal of Mathematical Chemistry

, Volume 57, Issue 1, pp 180–189 | Cite as

The edge-Hosoya polynomial of benzenoid chains

  • Niko TratnikEmail author
  • Petra Žigert Pleteršek
Original Paper
  • 59 Downloads

Abstract

The Hosoya polynomial is a well known vertex-distance based polynomial, closely correlated to the Wiener index and the hyper-Wiener index, which are widely used molecular-structure descriptors. In the present paper we consider the edge version of the Hosoya polynomial. For a connected graph G let \(d_e(G,k)\) be the number of (unordered) edge pairs at distance k. Then the edge-Hosoya polynomial of G is \(H_e(G,x) = \sum _{k \ge 0} d_e(G,k)\,x^k\). We investigate the edge-Hosoya polynomial of important chemical graphs known as benzenoid chains and derive the recurrence relations for them. These recurrences are then solved for linear benzenoid chains, which are also called polyacenes.

Keywords

Edge-Hosoya polynomial Benzenoid chain Polyacene 

Mathematics Subject Classification

92E10 05C12 

Notes

Acknowledgements

The authors acknowledge the financial support from the Slovenian Research Agency, research core funding Nos. P1-0297 and J1-9109.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of Natural Sciences and MathematicsUniversity of MariborMariborSlovenia
  2. 2.Faculty of Chemistry and Chemical EngineeringUniversity of MariborMariborSlovenia

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