  For a nonabelian group G, the non-commuting graph $\Gamma_G$ 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 $\Gamma_G$ 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 $D_{2n}$.
