The Intersection Graph of a Dihedral Group

The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j are said to be adjacent if and only if H_i ∩ H_j ≠ {e} . This study discusses the intersection graph of a dihedral group D₂ₙ specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D₂ₙ is containing complete subgraph Kₚ₊₂ and γ(Γ_{D₂ₙ})=p.