Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
DE
EN
Books
Journals
Events
Topic Page
Marketing
Log in
Learn more about individual access
Request company access
Electric Powertrains and Energy Systems 2025 | 26 + 27 March 2025

19th International MTZ Congress on Future Powertrains

Take this opportunity to attend the conference. Experts from the automotive industry, energy providers, and grid operators will meet up with representatives from politics and science to discuss important topics for this sector.
EXTENDED SEARCH
Log in
Top
Published in:
Read chapter Read first chapter

2024 | OriginalPaper | Chapter

The Vertex Degree of Relative G-Noncommuting Graph of the Dihedral Groups

Authors : Nur’Ain Supu, Intan Muchtadi Alamsyah, Erma Suwastika

Published in: Applied and Computational Mathematics

Publisher: Springer Nature Singapore

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Let G be a finite group, H be a subgroup of G, and g be a fixed element of G. The relative g-noncommuting graph \(\Gamma _{g, H, G}\) of G is defined as a graph with the vertex set G where two distinct vertices x and y are adjacent if \([x,y] \ne g\) and \([x,y] \ne g^{-1}\), and at least one of x or y belongs to H. This paper will discuss the vertex degree of the relative g-noncommuting graph for the dihedral group \(D_{2n}\), focusing specifically on cases where n is an even number. In this dihedral group, only two types of subgroups will be discussed, namely \(H=\langle a\rangle \) and \(H=\{e, a^j b \mid a,b \in G \}\) for some \(j=0,1, \dots , n-1\). Additionally, we will examine several topological indices of the relative g-noncommuting graph, including the first Zagreb index, the Wiener index, the edge Wiener index, the Hyper Wiener index, and the Harary index.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Nonlocal Edge Metric Dimension on Corona Multiproduct Graphs
next chapter On Conformable Fractional Riesz Bounded Variation of Order
Literature
1.
Abdollahi, A., Akbari, S., Maimani, H.R.: Non-commuting graph of a group. J. Algebra 298, 468–492 (2006)
2.
Alimon, N.I., Sarmin, N.H., Erfanian, A.: Topological indices of non-commuting graph of dihedral groups. Malays. J. Fundamental Appl. Sci. 473–476 (2018)
3.
Dankelman, P., Gutman, I., Mukwembi, S., Swart, H.C.: The Edge-Wiener index of a graph. Discrete Math. 309, 3452–3457 (2009)MathSciNetCrossRef
4.
Diestel, R.: Graph Theory, 5th edn. Springer (2017)
5.
Dummit, D.S., Foote, R.M.: Abstract Algebra, 3rd edn. Wiley (2004)
6.
7.
Gutman, I., Polansky, O.: Mathematical Concepts in Organic Chemistry. Springer (1986)
8.
Hildebrandt, T.H.: Linear continuous functionals on the space (\(BV\)) with weak topologies. Proc. Amer. Math. Soc. 17, 658–664 (1966)MathSciNet
9.
Issacs, M.: Algebra A Graduate Course. American Mathematical Society (2009)
10.
Jahandideh, M., Sarmin, N.H., Omer, S.M.S.: The topological indices of non-commuting graph of a finite group. Int. J. Pure Appl. Math. 105(1), 27–38 (2015)CrossRef
11.
Maulana, F., Alamsyah, I.M., Suwastika, E.: Topological Indices of Zero Divisor Graph of \({\bf Z}_{p^{n}}\) dan \({\bf Z}_{p^{n}} \times {\bf Z}_{q^{m}}\). Master’s Program Thesis, Institut Teknologi Bandung (2022)
12.
Nasiri, M., Erfanian, A., Alamsyah, I.M.: Kind of graph associated to a fixed element and a subgroup of group. Southeast Asian Bull. Math. 44(6), 813–818 (2020)MathSciNet
13.
Raza, Z., Faizi, S.: Non-commuting graph of finitely presented group. Sci. Int. (Lahore) 25, 883–885 (2013)
14.
Samaila, D., Ibrahim, B., Pur, M.P.: On the conjugacy classes, centers, and representation of the groups \(S_{n}\) and \(D_{n}\). Int. J. Pure Appl. Sci. Technol. 15(1), 87–95 (2013)
15.
Sharma, M., Nath, R.K.: Relative g-noncommuting graph of finite group. Electron. J. Graph Theory Appl. 10(1), 113–130 (2022)MathSciNetCrossRef
16.
Wiener, H.: Structural determination of paraffin boiling points. J. Am. Chem. Soc. 69(1), 17–20 (1947)CrossRef
17.
Metadata
Title
The Vertex Degree of Relative G-Noncommuting Graph of the Dihedral Groups
Authors
Nur’Ain Supu
Intan Muchtadi Alamsyah
Erma Suwastika
Copyright Year
2024
Publisher
Springer Nature Singapore
Book
Applied and Computational Mathematics

Print ISBN: 978-981-9721-35-1

Electronic ISBN: 978-981-9721-36-8

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-981-97-2136-8_26

Premium Partners

    Image Credits