Relations and bounds for the zeros of graph polynomials using vertex orbits

Research output: Contribution to journalArticleScientificpeer-review


  • Matthias Dehmer
  • Frank Emmert-Streib
  • Abbe Mowshowitz
  • Aleksandar Ilić
  • Zengqiang Chen
  • Guihai Yu
  • Lihua Feng
  • Modjtaba Ghorbani
  • Kurt Varmuza
  • Jin Tao

Research units

  • Swiss Distance University of Applied Sciences
  • Nankai University
  • Private University for Health Sciences, Medical Informatics and Technology
  • Tampere University
  • Facebook Inc
  • Guizhou University of Finance and Economics
  • Teacher Training University
  • Vienna University of Technology
  • Peking University
  • City College of New York


In this paper, we prove bounds for the unique, positive zero of OG (z):=1−OG(z), where OG(z) is the so-called orbit polynomial [1]. The orbit polynomial is based on the multiplicity and cardinalities of the vertex orbits of a graph. In [1], we have shown that the unique, positive zero δ ≤ 1 of OG (z) can serve as a meaningful measure of graph symmetry. In this paper, we study special graph classes with a specified number of orbits and obtain bounds on the value of δ.


Original languageEnglish
Article number125239
Number of pages14
JournalApplied Mathematics and Computation
Publication statusPublished - 1 Sep 2020
MoE publication typeA1 Journal article-refereed

    Research areas

  • Data science, Graph measures, Graphs, Networks, Quantitative graph theory, Symmetry

ID: 42833572