A few remarks on the theory of non-nilpotent graphs

Abstract

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