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arXiv · 2103.15574

The Cyclic Graph of a $2$-Frobenius Group

David G. Costanzo·Mark L. Lewis
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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.

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David G. Costanzo, Mark L. Lewis. 2021-03-29. The Cyclic Graph of a $2$-Frobenius Group. https://arxiv.org/abs/2103.15574

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