On the Non-Commuting Graph of Dihedral Group

Abstract

For a nonabelian group G, the non-commuting graph Γ G 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 G are adjacent if they do not commute in G. In this paper, we investigate the detour index, eccentric connectivity and total eccentricity polynomials of non-commuting graph on D 2n . We also find the mean distance of non-commuting graph on D 2n .