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

^*Corresponding author for this work

Shahid Rajaee Teacher Training University
Swiss Distance University of Applied Science
Private University for Health Sciences, Medical Informatics and Technology
Nankai University
Tampere University

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

5 Citations (Scopus)

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 - 7 Oct 2020
Externally published	Yes

Keywords

Automorphism group
Group action
Orbit
Orbit-stabilizer theorem
Polynomial roots

Access to Document

10.3390/sym12101643

Cite this

@article{b6529283e4e647dfbc483ff2b62ca418,

title = "On the degeneracy of the orbit polynomial and related graph polynomials",

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",

note = "Publisher Copyright: {\textcopyright} 2020 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2020",

month = oct,

day = "7",

doi = "10.3390/sym12101643",

language = "English",

volume = "12",

pages = "1--11",

journal = "Symmetry",

issn = "2073-8994",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "10",

}

TY - JOUR

T1 - On the degeneracy of the orbit polynomial and related graph polynomials

AU - Ghorbani, Modjtaba

AU - Dehmer, Matthias

AU - Emmert-Streib, Frank

PY - 2020/10/7

Y1 - 2020/10/7

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

UR - https://www.scopus.com/pages/publications/85093832766

U2 - 10.3390/sym12101643

DO - 10.3390/sym12101643

M3 - Article

AN - SCOPUS:85093832766

SN - 2073-8994

VL - 12

SP - 1

EP - 11

JO - Symmetry

JF - Symmetry

IS - 10

M1 - 1643

ER -

On the degeneracy of the orbit polynomial and related graph polynomials

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this