Graph Theory With Applications
Graph Theory With Applications
| Hi-index | 0.04 |
The non-commuting graph @C"G of a non-abelian group G is defined as follows. The vertex set of @C"G is G-Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xyyx. It has been conjectured that if G and H are two non-abelian finite groups such that @C"G@?@C"H, then |G|=|H| and moreover in the case that H is a simple group this implies G@?H. In this paper, our aim is to prove the first part of the conjecture for all the finite non-abelian simple groups H. Then for certain simple groups H, we show that the graph isomorphism @C"G@?@C"H implies G@?H.