There are various graphs connected with algebraic structures that can be used to study some of their properties. Intersection graphs are one of them, and they have been explored extensively in the literature over the last fifty years. The intersection graph of F is a graph having two vertices vi and vj in F which are adjacent if and only if ???????? ≠ ???????? and ???????? ∩ ???????? ≠ ∅. Meanwhile, a graph of subgroups of a group is a graph whose vertices are the subgroups of the group. In this research, we define the cyclic intersection graph of subgroups of G as follows: Let G be a group, the cyclic intersection graph of subgroups of a group, denoted by ????∩ ???? (G), is a graph having all nontrivial subgroups, as its vertices and two vertices H and K are adjacent if and only if H intersection K is a non-trivial cyclic subgroup.

Keywords