On the zeros of the partial Hosoya polynomial of graphs

Modjtaba Ghorbani*, Matthias Dehmer, Shujuan Cao, Lihua Feng, Jin Tao, Frank Emmert-Streib

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

The partial Hosoya polynomial (or briefly the partial H-polynomial) can be used to construct the well-known Hosoya polynomial. The ith coefficient of this polynomial, defined for an arbitrary vertex u of a graph G, is the number of vertices at distance i from u. The aim of this paper is to determine the partial H-polynomial of several well-known graphs and, then, to investigate the location of their zeros. To pursue, we characterize the structure of graphs with the minimum and the maximum modulus of the zeros of partial H-polynomial. Finally, we define another graph polynomial of the partial H-polynomial, see [9]. Also, we determine the unique positive root of this polynomial for particular graphs.

Original languageEnglish
Pages (from-to)199-215
Number of pages17
JournalInformation Sciences
Volume524
DOIs
Publication statusPublished - Jul 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Cut-vertex
  • Distance
  • Hosoya polynomial
  • Polynomial roots

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    Ghorbani, M., Dehmer, M., Cao, S., Feng, L., Tao, J., & Emmert-Streib, F. (2020). On the zeros of the partial Hosoya polynomial of graphs. Information Sciences, 524, 199-215. https://doi.org/10.1016/j.ins.2020.03.011