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Salahshour, Mohammad Ali, Ashrafi, Ali Reza. (1403). Commuting Conjugacy Class Graph of The Finite $2-$Groups $G_n(m)$ and $G[n]$. , 13(2), 67-71. doi: 10.22103/jmmr.2023.21431.1436
Mohammad Ali Salahshour; Ali Reza Ashrafi. "Commuting Conjugacy Class Graph of The Finite $2-$Groups $G_n(m)$ and $G[n]$". , 13, 2, 1403, 67-71. doi: 10.22103/jmmr.2023.21431.1436
Salahshour, Mohammad Ali, Ashrafi, Ali Reza. (1403). 'Commuting Conjugacy Class Graph of The Finite $2-$Groups $G_n(m)$ and $G[n]$', , 13(2), pp. 67-71. doi: 10.22103/jmmr.2023.21431.1436
Salahshour, Mohammad Ali, Ashrafi, Ali Reza. Commuting Conjugacy Class Graph of The Finite $2-$Groups $G_n(m)$ and $G[n]$. , 1403; 13(2): 67-71. doi: 10.22103/jmmr.2023.21431.1436

Commuting Conjugacy Class Graph of The Finite $2-$Groups $G_n(m)$ and $G[n]$

Journal of Mahani Mathematical Research
دوره 13، شماره 2 - شماره پیاپی 27، آبان 2024، صفحه 67-71    اصل مقاله (489.58 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22103/jmmr.2023.21431.1436
نویسندگان
Mohammad Ali Salahshour* 1؛ Ali Reza Ashrafi2
1Department of Mathematics, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran
2Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
چکیده
‎Suppose $G$ is a finite non-abelian group and $\Gamma(G)$ is a graph with non-central conjugacy classes of $G$ as its vertex set. Two vertices $L$ and $K$ in $\Gamma(G)$ are adjacent if there are $a \in L$ and $b \in K$ such that $ab = ba$.    This graph  is called the commuting conjugacy class graph of $G$.  The purpose of this paper is to compute  the commuting conjugacy class graph of the finite $2-$groups $G_n(m)$ and $G[n]$.
کلیدواژه‌ها
Commuting conjugacy class graph‎؛ ‎conjugacy class‎؛ ‎center
مراجع
[1] A. R. Ashra  and M. A. Salahshour, Counting Centralizers of a Finite Group with an Application in Constructing the Commuting Conjugacy Class Graph, Communications in Algebra, 51 (3) (2023), 1105{1116.

[2] F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.

[3] M. Herzog, P. Longobardi and M. Maj, On a commuting graph on conjugacy classes of groups, Comm. Algebra, 37 (10) (2009) 3369{3387.

[4] A. R. Jamali, Some new non-abelian 2-groups with abelian automorphism groups, J. Group Theory, 5 (2002) 53{57.

[5] G. A. Miller, A non-abelian group whose group of isomorphisms is abelian, Messenger Math., 43 (1913) 124{125.

[6] A. Mohammadian, A. Erfanian, M. Farrokhi D. G. and B. Wilkens, Triangle-free commuting conjugacy class graphs, J. Group Theory, 19 (3) (2016) 1049{1061.

[7] D. J. S. Robinson, A Course in the Theory of Groups, 2nd ed., Springer, Berlin, 1982.

[8] R. R. Struik, Some non-abelian 2-groups with abelian automorphism groups, Arch. Math., 39 (1982) 299{302.

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