| Abstrakt: |
For a finite non-cyclic group G, let Cyc(G) be the set of elements a of G such that (a,b) is cyclic for each b of G. The non-cyclic graph of G is the graph with vertex set G \ Cyc(G), two distinct vertices x and y are adjacent if (x,y) is not cyclic. In this paper, we characterize the full automorphism group of the non-cyclic graph of a finite group. As applications, we compute the full automorphism group of the non-cyclic graph of an elementary abelian group, a dihedral group, a semi-dihedral group, and a generalized quaternion group. [ABSTRACT FROM AUTHOR] |
