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Abstract
In a graph theory we have use basis of the group like abelian group and subgroup for intersection and complete. We characterize certain classes of subgroup intersection graphs are complete. We check all its solvable groups whose intersection graphs are complete. Surrounded the other results, we analysis all abelian groups whose intersection graphs are complete. Finally, we study the intersection graphs of cyclic groups. In this section, we study the groups whose intersection graphs are complete.