On the maximal independence polynomial of certain graph configurations

Han Hu, Toufik Mansour, Chunwei Song

Research output: Contribution to journalArticlepeer-review


In this paper, we investigate the maximal independence polynomials of some popular graph configurations. Through careful analysis, some of the polynomials under study are shown to be Chebyshev, which helps characterize polynomial properties such as unimodality, log-concavity and real-rootedness with ease and efficiency. We partially characterize the bridge path and bridge cycle graphs of wheels and fans according to their unimodality properties and propose relevant open problems. Also, to compare with the usual independence polynomials, we provide analogous results regarding the vertebrated graph, and the firecracker graph, as studied by Wang and Zhu [47].

Original languageEnglish
Pages (from-to)2219-2253
Number of pages35
JournalRocky Mountain Journal of Mathematics
Issue number7
StatePublished - 2017

Bibliographical note

Publisher Copyright:
Copyright © 2017 Rocky Mountain Mathematics Consortium.


  • Bridge cycle
  • Bridge path
  • Chebyshev polynomial
  • Maximal independence
  • Recurrence
  • Unimodality

ASJC Scopus subject areas

  • General Mathematics


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