Crosscap of the non-cyclic graph of groups. Issue 3 (1st December 2016) - Selvakumar, K.; Subajini, M.
Abstract: The non-cyclic graph C G to a non locally cyclic group G is as follows: take G ∖ C y c ( G ) as vertex set, where C y c ( G ) = { x ∈ G | 〈 x, y 〉 is cyclic for all y ∈ G } is called the cyclicizer of G, and join two vertices if they do not generate a cyclic subgroup. In this paper, we classify the finite groups whose non-cyclic graphs are outerplanar. Also all finite groups whose non-cyclic graphs can be embedded on the torus or projective plane are classified.