A few remarks on the theory of non-nilpotent graphs

–We prove a few results about non-nilpotent graphs of symmetric groups Sn – namely that they satisfy conjecture Nongsiang and Saikia (which is likewise proved for alternating An), n⩾19 each vertex has degree at least n!2. We also show the class does not have any “local” properties, i.e. every simple graph X there group G, such its contains as an induced subgraph.