On the non-commuting graph of dihedral group

Abstract

For a nonabelian group G, the non-commuting graph ΓGof 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 ΓGare 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.