On the non-commuting graph of dihedral group

Sanhan Muhammad Salih Khasraw (Department of Mathematics, College of Education, Salahaddin University-Erbil, Erbil, Kurdistan Region, Iraq)
Ivan Dler Ali (Department of Mathematics, College of Education, Salahaddin University-Erbil, Erbil, Kurdistan Region, Iraq)
Rashad Rashid Haji (Department of Mathematics, College of Education, Salahaddin University-Erbil, Kurdistan Region, Iraq)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications

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.