  For a group $G$, the generating graph $\Gamma(G)$ is defined as the graph
with the vertex set $G$, and any two distinct vertices of $\Gamma(G)$ are
adjacent if they generate $G$. In this paper, we study the generating graph of
$D_n,$ where $D_n$ is a Dihedral group of order $2n$. We explore various graph
theoretic properties, and determine complete spectrum of the adjacency and the
Laplacian matrix of $\Gamma(D_n)$. Moreover, we compute some distance and
degree based topological indices of $\Gamma(D_n)$.
