  Let $G$ be a simple, connected graph, $\mathcal{D}(G)$ be the distance matrix
of $G$, and $Tr(G)$ be the diagonal matrix of vertex transmissions of $G$. The
distance Laplacian matrix and distance signless Laplacian matrix of $G$ are
defined by $\mathcal{L}(G) = Tr(G)-\mathcal{D}(G)$ and $\mathcal{Q}(G) =
Tr(G)+\mathcal{D}(G)$, respectively. The eigenvalues of $\mathcal{D}(G)$,
$\mathcal{L}(G)$ and $\mathcal{Q}(G)$ is called the $\mathcal{D}-$spectrum,
$\mathcal{L}-$spectrum and $\mathcal{Q}-$spectrum, respectively. The
generalized distance matrix of $G$ is defined as
$\mathcal{D}_{\alpha}(G)=\alpha
Tr(G)+(1-\alpha)\mathcal{D}(G),~0\leq\alpha\leq1$, and the generalized distance
spectral radius of $G$ is the largest eigenvalue of $\mathcal{D}_{\alpha}(G)$.
In this paper, we give a complete description of the $\mathcal{D}-$spectrum,
$\mathcal{L}-$spectrum and $\mathcal{Q}-$spectrum of some graphs obtained by
operations. In addition, we present some new upper and lower bounds on the
generalized distance spectral radius of $G$ and of its line graph $L(G)$, based
on other graph-theoretic parameters, and characterize the extremal graphs.
Finally, we study the generalized distance spectrum of some composite graphs.
