  For a simple connected graph $G$, let $D(G)$, $Tr(G)$, $D^{L}(G)$ and
$D^{Q}(G)$, respectively be the distance matrix, the diagonal matrix of the
vertex transmissions, distance Laplacian matrix and the distance signless
Laplacian matrix of a graph $G$. The convex linear combinations $D_{\alpha}(G)$
of $Tr(G)$ and $D(G)$ is defined as $D_{\alpha}(G)=\alpha
Tr(G)+(1-\alpha)D(G)$, $0\leq \alpha\leq 1$. As $D_{0}(G)=D(G), ~~~
2D_{\frac{1}{2}}(G)=D^{Q}(G), ~~~ D_{1}(G)=Tr(G)$ and
$D_{\alpha}(G)-D_{\beta}(G)=(\alpha-\beta)D^{L}(G)$, this matrix reduces to
merging the distance spectral, distance Laplacian spectral and distance
signless Laplacian spectral theories. Let $\partial_{1}(G)\geq
\partial_{2}(G)\geq \dots \geq \partial_{n}(G)$ be the eigenvalues of
$D_{\alpha}(G)$ and let $D_{\alpha}S(G)=\partial_{1}(G)-\partial_{n}(G)$ be the
generalized distance spectral spread of the graph $G$. In this paper, we obtain
some bounds for the generalized distance spectral spread $D_{\alpha}(G)$. We
also obtain relation between the generalized distance spectral spread
$D_{\alpha}(G)$ and the distance spectral spread $S_{D}(G)$. Further, we obtain
the lower bounds for $D_{\alpha}S(G)$ of bipartite graphs involving different
graph parameters and we characterize the extremal graphs for some cases. We
also obtain lower bounds for $D_{\alpha}S(G)$ in terms of clique number and
independence number of the graph $G$ and characterize the extremal graphs for
some cases.
