Geodesic
Groups with symmetric non-commuting graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 645-653 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we characterize non-abelian finite $2$-generator groups $G$ whose non-commuting graphs are $\mathrm{Aut}(G)$-symmetric. We also find some general results on these groups. These partially answer Problem 31 posed in Peter Cameron's home page, old problems.
Keywords: non-commuting graph, symmetric graphs.
Mots-clés : automorphism group 
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A. Abdollahi. Groups with symmetric non-commuting graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 645-653. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a2/

[1] A. Abdollahi, A. Akbari, H.R. Maimani, “Non-commuting graph of a group”, J. Algebra, 298:2 (2006), 468–492 | DOI | MR | Zbl

[2] A.R. Moghaddamfar, W. Shi, W. Zhou, A.R. Zokayi, “On the noncommuting graph associated with a finite group”, Sib. Math. J., 46:2 (2005), 325–332 | DOI | MR | Zbl

[3] Peter Cameron's Home page, Old Problems, https://cameroncounts.github.io/web/QM/

[4] D.J.S. Robinson, A course in the theory of groups, 2nd Ed., Springer, New York, 1995 | MR | Zbl