On the non-cyclic graph of a group

Abstract

Here we study some algebraic properties of non-cyclic graphs. In this paper, we show that [Formula: see text] is isomorphic to [Formula: see text] or [Formula: see text] if and only if [Formula: see text] is isomorphic to [Formula: see text] or [Formula: see text], respectively. We characterize all groups of order [Formula: see text] like [Formula: see text] in which [Formula: see text], where [Formula: see text].