Geodesic
On the intersection graph of a finite group
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 4, pp. 1145-1153 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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For a finite group $G$, the intersection graph of $G$ which is denoted by $\Gamma (G)$ is an undirected graph such that its vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H\cap K\neq 1$. In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of ${\rm Aut}(\Gamma (G))$.
For a finite group $G$, the intersection graph of $G$ which is denoted by $\Gamma (G)$ is an undirected graph such that its vertices are all nontrivial proper subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent when $H\cap K\neq 1$. In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of ${\rm Aut}(\Gamma (G))$.
DOI : 10.21136/CMJ.2017.0446-16
Classification : 05C25, 20E32
Keywords: intersection graph; regular graph; simple group; automorphism group 
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Shahsavari, Hossein; Khosravi, Behrooz. On the intersection graph of a finite group. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 4, pp. 1145-1153. doi: 10.21136/CMJ.2017.0446-16

[1] Akbari, S., Heydari, F., Maghasedi, M.: The intersection graph of a group. J. Algebra Appl. 14 (2015), Article ID 1550065, 9 pages. | DOI | MR | JFM

[2] Ballester-Bolinches, A., Esteban-Romero, R., Robinson, D. J. S.: On finite minimal non-nilpotent groups. Proc. Am. Math. Soc. 133 (2005), 3455-3462. | DOI | MR | JFM

[3] Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., Wilson, R. A.: Atlas of Finite Groups. Maximal Subgroups and Ordinary Characters for Simple Groups. Clarendon Press, Oxford (1985). | MR | JFM

[4] Csákány, B., Pollák, G.: The graph of subgroups of a finite group. Czech. Math. J. 19 (1969), 241-247 Russian. | MR | JFM

[5] M. Hall, Jr.: The Theory of Groups. Chelsea Publishing Company, New York (1976). | MR | JFM

[6] Kayacan, S., Yaraneri, E.: Abelian groups with isomorphic intersection graphs. Acta Math. Hung. 146 (2015), 107-127. | DOI | MR | JFM

[7] Kayacan, S., Yaraneri, E.: Finite groups whose intersection graphs are planar. J. Korean Math. Soc. 52 (2015), 81-96. | DOI | MR | JFM

[8] King, C. S. H.: Generation of finite simple groups by an involution and an element of prime order. J. Algebra 478 (2017), 153-173. | DOI | MR | JFM

[9] Ma, X.: On the diameter of the intersection graph of a finite simple group. Czech. Math. J. 66 (2016), 365-370. | DOI | MR | JFM

[10] Robinson, D. J. S.: A Course in the Theory of Groups. Graduate Texts in Mathematics 80, Springer, New York (1996). | DOI | MR | JFM

[11] Shen, R.: Intersection graphs of subgroups of finite groups. Czech. Math. J. 60 (2010), 945-950. | DOI | MR | JFM

[12] Zelinka, B.: Intersection graphs of finite abelian groups. Czech. Math. J. 25 (1975), 171-174. | MR | JFM

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