Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 47 Sayı: 1, 93 - 99, 01.02.2018

Öz

Kaynakça

  • A. Abdollahi, S. Akbari and H. R. Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006), 468-492.
  • A. Abdollahi, Engel graph associated with a group, J. Algebra, 318 (2007), 680-691.
  • A. Abdollahi and A. Mohammadi Hassanabadi, Non-cyclic graph of a group, Comm. in Algebra, 35 (2007), 2057-2081.
  • R. Barzegar and A. Erfanian, Nilpotency and solubility of groups relative to an automorphism, Caspian Journal of Mathematical Sciences, 4(2) (2015), 271-283.
  • A. Erfanian, M. Farrokhi D.G. and B. Tolue, Non-normal graphs of finite groups, J. Algebra Appl., 12 (2013).
  • J. A. Bondy and J. S. R. Murty, Graph Theory with Applications, Elsevier, (1977).
  • P. J. Cameron and S. Ghosh, The power graph of a fnite group, Discrete Math, 311 (2011), 1220-1222.
  • I. Fabrici and T. Madaras, The structure of 1-planar graphs, Discrete Mathematics, 307 (2007), 854 - 865.
  • A. Iranmanesh and A. Jafarzadeh, On the commuting graph associated with the symmetric and alternating groups, J. Algebra Appl., 7 (2008), 129-146.
  • D. J. S. Robinson, A Course in the Theory of Groups, Springer-Verlag: New York-Heidelberg Berlin (1982).
  • The GAP Group, GAP-Groups, Algorithms and Programming, Version 4.6.4, 2013 (http://www.gap-system.org/).
  • J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 (2) (1981), 487-513.

A graph associated to a fixed automorphism of a finite group

Yıl 2018, Cilt: 47 Sayı: 1, 93 - 99, 01.02.2018

Öz

Let $G$ be a finite group and $Aut(G)$ be the group of automorphisms of $G$. We associate a graph to a group $G$ and fixed automorphism $\alpha$ of $G$ denoted by $\Gamma_G^\alpha$. The vertex set of $\Gamma_G^\alpha$ is $G\backslash Z^\alpha(G)$ and two vertices $x,g\in G\backslash Z^\alpha(G)$ are adjacent if $[g,x]_\alpha\neq 1$ or $[x,g]_\alpha\neq 1$, where $[g,x]_\alpha=g^{-1}x^{-1}gx^\alpha$ and $Z^\alpha(G)=\{ x\in G\,|\, [g,x]_\alpha=1\,\,\textrm{for all}\,\, g\inG \}$. In this paper, we state some basic properties of the graph, like connectivity, diameter, girth and Hamiltonian. Moreover, planarity and 1-planarity are also investigated here.

Kaynakça

  • A. Abdollahi, S. Akbari and H. R. Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006), 468-492.
  • A. Abdollahi, Engel graph associated with a group, J. Algebra, 318 (2007), 680-691.
  • A. Abdollahi and A. Mohammadi Hassanabadi, Non-cyclic graph of a group, Comm. in Algebra, 35 (2007), 2057-2081.
  • R. Barzegar and A. Erfanian, Nilpotency and solubility of groups relative to an automorphism, Caspian Journal of Mathematical Sciences, 4(2) (2015), 271-283.
  • A. Erfanian, M. Farrokhi D.G. and B. Tolue, Non-normal graphs of finite groups, J. Algebra Appl., 12 (2013).
  • J. A. Bondy and J. S. R. Murty, Graph Theory with Applications, Elsevier, (1977).
  • P. J. Cameron and S. Ghosh, The power graph of a fnite group, Discrete Math, 311 (2011), 1220-1222.
  • I. Fabrici and T. Madaras, The structure of 1-planar graphs, Discrete Mathematics, 307 (2007), 854 - 865.
  • A. Iranmanesh and A. Jafarzadeh, On the commuting graph associated with the symmetric and alternating groups, J. Algebra Appl., 7 (2008), 129-146.
  • D. J. S. Robinson, A Course in the Theory of Groups, Springer-Verlag: New York-Heidelberg Berlin (1982).
  • The GAP Group, GAP-Groups, Algorithms and Programming, Version 4.6.4, 2013 (http://www.gap-system.org/).
  • J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 (2) (1981), 487-513.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

M. Mahtabi Bu kişi benim

A. Erfanian

Yayımlanma Tarihi 1 Şubat 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 47 Sayı: 1

Kaynak Göster

APA Mahtabi, M., & Erfanian, A. (2018). A graph associated to a fixed automorphism of a finite group. Hacettepe Journal of Mathematics and Statistics, 47(1), 93-99.
AMA Mahtabi M, Erfanian A. A graph associated to a fixed automorphism of a finite group. Hacettepe Journal of Mathematics and Statistics. Şubat 2018;47(1):93-99.
Chicago Mahtabi, M., ve A. Erfanian. “A Graph Associated to a Fixed Automorphism of a Finite Group”. Hacettepe Journal of Mathematics and Statistics 47, sy. 1 (Şubat 2018): 93-99.
EndNote Mahtabi M, Erfanian A (01 Şubat 2018) A graph associated to a fixed automorphism of a finite group. Hacettepe Journal of Mathematics and Statistics 47 1 93–99.
IEEE M. Mahtabi ve A. Erfanian, “A graph associated to a fixed automorphism of a finite group”, Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 1, ss. 93–99, 2018.
ISNAD Mahtabi, M. - Erfanian, A. “A Graph Associated to a Fixed Automorphism of a Finite Group”. Hacettepe Journal of Mathematics and Statistics 47/1 (Şubat 2018), 93-99.
JAMA Mahtabi M, Erfanian A. A graph associated to a fixed automorphism of a finite group. Hacettepe Journal of Mathematics and Statistics. 2018;47:93–99.
MLA Mahtabi, M. ve A. Erfanian. “A Graph Associated to a Fixed Automorphism of a Finite Group”. Hacettepe Journal of Mathematics and Statistics, c. 47, sy. 1, 2018, ss. 93-99.
Vancouver Mahtabi M, Erfanian A. A graph associated to a fixed automorphism of a finite group. Hacettepe Journal of Mathematics and Statistics. 2018;47(1):93-9.