Results 11 to 20 of about 2,044 (191)
On the non-commuting graph of dihedral group [PDF]
Electronic Journal of Graph Theory and Applications, 2020 For a nonabelian group G, the non-commuting graph Γ of G is defined as the graph with vertex-set G-Z(G), where Z(G) is the center of G, and two distinct vertices of Γ are adjacent if they do not commute in G.
Sanhan Muhammad Salih Khasraw +2 more
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ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS [PDF]
Journal of Algebraic Systems, 2015 Let $G$ be a non-abelian finite group. In this paper, we prove that $Gamma(G)$ is $K_4$-free if and only if $G cong A times P$, where $A$ is an abelian group, $P$ is a $2$-group and $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$.
Neda Ahanjideh, Hajar Mousavi
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Non-Commuting Graphs of Nilpotent Groups [PDF]
Communications in Algebra, 2014 5 pages; to appear in Comm ...
Alireza Abdollahi
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Non-commuting graph of a group
Journal of Algebra, 2006 The non-commuting graph \(\Gamma_G\) of a non-Abelian group \(G\) is defined as follows. The vertex set of \(\Gamma_G\) is \(V(G)=G-Z(G)\) and two vertices \(x\) and \(y\) are joined by an edge if and only if \(xy\neq yx\). This graph was first defined by P. Erdős which is quoted by \textit{B. H. Neumann} [J. Aust. Math. Soc., Ser. A 21, 467-472 (1976;
Alireza Abdollahi +2 more
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On the relation between the non-commuting graph and the prime graph [PDF]
International Journal of Group Theory, 2012 Given a non-abelian finite group $G$, let $pi(G)$ denote the set of prime divisors of the order of $G$ and denote by $Z(G)$ the center of $G$. Thetextit{ prime graph} of $G$ is the graph with vertex set $pi(G)$ where two distinct primes $p$ and $q$ are ...
N. Ahanjideh, A. Iranmanesh
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Groups with the same non-commuting graph
Discrete Applied Mathematics, 2009 Let \(G\) be a non-Abelian group and associate a non-commuting graph \(\nabla(G)\) with \(G\) as follows: the vertex set of \(\nabla(G)\) is \(G\setminus Z(G)\) where \(Z(G)\) denotes the center of \(G\) and two vertices \(x\) and \(y\) are adjacent if and only if \(xy\neq yx\).
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Domination number of the non-commuting graph of finite groups [PDF]
Electronic Journal of Graph Theory and Applications, 2018 Let G be a non-abelian group. The non-commuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are adjacent whenever ab ≠ ba.
Ebrahim Vatandoost, Masoumeh Khalili
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The rainbow k-connectivity of the non-commutative graph of a finite group [PDF]
Electronic Journal of Graph Theory and Applications, 2020 The non-commuting graph Γ(G) of a non-abelian group G is defined as follows. The vertex set V(Γ(G)) of ℾ(G) is G \ Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xy ≠ yx.
Luis A. Dupont +2 more
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Laplacian Spectrum of Non-Commuting Graphs of Finite Groups [PDF]
Indian Journal of Pure and Applied Mathematics, 2018 arXiv admin note: text overlap with arXiv:1604 ...
Rajat Kanti Nath, Nath Rajat Kanti
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Characterization of the alternating group by its non-commuting graph
Journal of Algebra, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alireza Abdollahi
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