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

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Original languageEnglish
Article number125239
JournalApplied Mathematics and Computation
Publication statusPublished - 1 Sep 2020
Publication typeA1 Journal article-refereed


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.


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

Publication forum classification

Field of science, Statistics Finland