Geodesic
Finite groups whose commuting graph is split
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 1, pp. 280-283 Cet article a éte moissonné depuis la source Math-Net.Ru

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As a contribution to the study of graphs defined on groups, we show that for a finite group $G$ the following statements are equivalent{:} the commuting graph of $G$ is a split graph; the commuting graph of $G$ is a threshold graph; either $G$ is abelian, or $G$ is a generalized dihedral group $D(A)=\langle A,t:(\forall a\in A)(at)^2=1\rangle$ where $A$ is an abelian group of odd order.
Keywords: сommuting graph, split graph, threshold graph, generalized dihedral group. 
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Xuanlong Ma; Peter J. Cameron. Finite groups whose commuting graph is split. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 30 (2024) no. 1, pp. 280-283. http://geodesic.mathdoc.fr/item/TIMM_2024_30_1_a20/

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