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arXiv · 2210.00344

A few remarks on the theory of non-nilpotent graphs

Radosław Żak
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Abstract

We prove a few results about non-nilpotent graphs of symmetric groups $S_n$ -- namely that they have a Hamiltonian cycle and they satisfy a conjecture of Nongsiang and Saikia. The latter is likewise proven for alternating groups $A_n$. We also show that the class of non-nilpotent graphs does not have any ''local'' properties, ie. for every simple graph $X$ there is a group $G$, such that its non-nilpotent graph has $X$ as an induced subgraph.

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Radosław Żak. 2022-10-01. A few remarks on the theory of non-nilpotent graphs. https://doi.org/10.1080/00927872.2023.2213771

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