Groups for which the noncommuting graph is a split graph

The noncommuting graph \nabla (G) of a group G is a simple graph whose vertex set is the set of noncentral elements of G and the edges of which are the ones connecting two noncommuting elements. We determine here, up to isomorphism, the structure of any finite nonabeilan group G whose noncommuting graph is a split graph, that is, a graph whose vertex set can be partitioned into two sets such that the induced subgraph on one of them is a complete graph and the induced subgraph on the other is an independent set.

Keywords:

nonabelian group , noncommuting graph , split graph