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

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

Applied Mathematics and Computation, 2020, vol. 380, issue C

Abstract: 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.

Keywords: Quantitative graph theory; Networks; Symmetry; Graphs; Graph measures; Data science (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302083

DOI: 10.1016/j.amc.2020.125239

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