Abstract
The cyclic graph of a group $G$ is the graph whose vertices are the nonidentity elements of $G$ and whose edges connect distinct elements $x$ and $y$ if and only if the subgroup $\langle x,y \rangle$ is cyclic. We obtain information about the cyclic graph of 2-Frobenius groups. The cyclic graph of a 2-Frobenius group is disconnected. In this paper, we determine the number of connected components of the cyclic graph of any 2-Frobenius group.
Acknowledgments
We thank the referee for carefully reading the initial manu- script and making helpful suggestions.
Citation
David G. Costanzo. Mark L. Lewis. "The Cyclic Graph of a 2-Frobenius Group." Albanian J. Math. 15 (1) 61 - 72, 2021. https://doi.org/10.51286/albjm/1608313774
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