Crosscap of the non-cyclic graph of groups. Issue 3 (1st December 2016)

• Record Type: Journal Article
• Authors: Selvakumar, K.; Subajini, M.
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 13:Issue 3(2016)
• Page Start: 235
• Page End: 240
• Publication Date: 2016-12-01
• Subjects: Non-cyclic group -- Non-cyclic graph -- Planar graph -- Genus -- Crosscap
• DOI: 10.1016/j.akcej.2016.06.013
• Languages: English
• ISSNs: 0972-8600

Abstract

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.