On the Commuting Graph of Dihedral Group

Let Γ be a non-abelian group and Ω ⊆ Γ. We define the commuting graph G = 𝒞(Γ, Ω) with vertex set Ω and two distinct elements of Ω are joined by an edge when they commute in Γ. In this article, among some properties of commuting graphs, we investigate distant properties as well as detour distant properties of commuting graph on D2n. We also study the metric dimension of commuting graph on D2n and compute its resolving polynomial.