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 $G/Z(G) cong mathbb{ Z}_2 times mathbb{Z}_2$. Also, we show that $Gamma(G)$ is $K_{1,3}$-free if and only if $G cong {mathbb{S}}_3,~D_8$ or $Q_8$.
Ahanjideh, N., & Mousavi, H. (2015). ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS. Journal of Algebraic Systems, 2(2), 147-151. doi: 10.22044/jas.2015.372
MLA
N. Ahanjideh; H. Mousavi. "ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS", Journal of Algebraic Systems, 2, 2, 2015, 147-151. doi: 10.22044/jas.2015.372
HARVARD
Ahanjideh, N., Mousavi, H. (2015). 'ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS', Journal of Algebraic Systems, 2(2), pp. 147-151. doi: 10.22044/jas.2015.372
VANCOUVER
Ahanjideh, N., Mousavi, H. ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS. Journal of Algebraic Systems, 2015; 2(2): 147-151. doi: 10.22044/jas.2015.372
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