Geodesic
On the commutation graph of cyclic TI-subgroup in an ortogonal group~$G$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 180-199

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We study the commutation graph $\Gamma _G(A)$ of cyclic TI-subgroup A of order 4 in a finite group G with quasisimple generalized Fitting subgroup $F^*(G)$. It is proved that, if $F^*(G)$ is a ortogonal group, then the graph $\Gamma _G(A)$ is edge-regular but not coedge-regular graph.
Keywords: finite group, cyclic TI-subgroup, commutation graph. 
@article{SEMR_2013_10_a6,
     author = {N. D. Zyulyarkina},
     title = {On the commutation graph of cyclic {TI-subgroup} in an ortogonal group~$G$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {180--199},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a6/}
}
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N. D. Zyulyarkina. On the commutation graph of cyclic TI-subgroup in an ortogonal group~$G$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 180-199. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a6/