On the degeneracy of the orbit polynomial and related graph polynomials

Modjtaba Ghorbani; Matthias Dehmer; Frank Emmert-Streib

doi:10.3390/sym12101643

On the degeneracy of the orbit polynomial and related graph polynomials

Modjtaba Ghorbani, Matthias Dehmer, Frank Emmert-Streib

Computing Sciences

Research output: Contribution to journal › Article › Scientific › peer-review

5 Citations (Scopus)

11 Downloads (Pure)

Abstract

The orbit polynomial is a new graph counting polynomial which is defined as (formula presented) where O₁, …, O_r are all vertex orbits of the graph G. In this article, we investigate the structural properties of the automorphism group of a graph by using several novel counting polynomials. Besides, we explore the orbit polynomial of a graph operation. Indeed, we compare the degeneracy of the orbit polynomial with a new graph polynomial based on both eigenvalues of a graph and the size of orbits.

Original language	English
Article number	1643
Pages (from-to)	1-11
Number of pages	11
Journal	Symmetry
Volume	12
Issue number	10
DOIs	https://doi.org/10.3390/sym12101643
Publication status	Published - Oct 2020
Publication type	A1 Journal article-refereed

Keywords

Automorphism group
Group action
Orbit
Orbit-stabilizer theorem
Polynomial roots

Publication forum classification

Publication forum level 1

ASJC Scopus subject areas

Computer Science (miscellaneous)
Chemistry (miscellaneous)
General Mathematics
Physics and Astronomy (miscellaneous)

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10.3390/sym12101643Licence: CC BY

symmetry-12-01643Final published version, 734 KBLicence: CC BY

http://urn.fi/URN:NBN:fi:tuni-202012148783Licence: CC BY

Cite this

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abstract = "The orbit polynomial is a new graph counting polynomial which is defined as (formula presented) where O1, …, Or are all vertex orbits of the graph G. In this article, we investigate the structural properties of the automorphism group of a graph by using several novel counting polynomials. Besides, we explore the orbit polynomial of a graph operation. Indeed, we compare the degeneracy of the orbit polynomial with a new graph polynomial based on both eigenvalues of a graph and the size of orbits.",

keywords = "Automorphism group, Group action, Orbit, Orbit-stabilizer theorem, Polynomial roots",

author = "Modjtaba Ghorbani and Matthias Dehmer and Frank Emmert-Streib",

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N2 - The orbit polynomial is a new graph counting polynomial which is defined as (formula presented) where O1, …, Or are all vertex orbits of the graph G. In this article, we investigate the structural properties of the automorphism group of a graph by using several novel counting polynomials. Besides, we explore the orbit polynomial of a graph operation. Indeed, we compare the degeneracy of the orbit polynomial with a new graph polynomial based on both eigenvalues of a graph and the size of orbits.

AB - The orbit polynomial is a new graph counting polynomial which is defined as (formula presented) where O1, …, Or are all vertex orbits of the graph G. In this article, we investigate the structural properties of the automorphism group of a graph by using several novel counting polynomials. Besides, we explore the orbit polynomial of a graph operation. Indeed, we compare the degeneracy of the orbit polynomial with a new graph polynomial based on both eigenvalues of a graph and the size of orbits.

KW - Automorphism group

KW - Group action

KW - Orbit

KW - Orbit-stabilizer theorem

KW - Polynomial roots

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On the degeneracy of the orbit polynomial and related graph polynomials

Abstract

Keywords

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