On the non-commuting graph of dihedral group - Sanhan Muhammad Salih Khasraw; Ivan Dler Ali; Rashad Rashid Haji (Electronic Journal of Graph Theory and Applications (EJGTA), 2020)
For a nonabelian group G, the non-commuting graph Γ of G is defined as the graph with vertex-set G-Z(G), where Z(G) is the center of G, and two distinct vertices of Γ are adjacent if they do not commute in G. In this paper, we investigate the detour index, eccentric connectivity and total eccentricity polynomials of the non-commuting graph on D2n. We also find the mean distance of the non-commuting graph on D2n.