  For a connected graph $G$, we present the concept of a new graph matrix
related to its distance and Seidel matrix, called distance Seidel matrix
$\mathcal{D}^S(G)$. Suppose that the eigenvalues of $\mathcal{D}^S(G)$ be
$\partial_{1}^{S}(G) \geq \cdots \geq \partial_{n}^{S}(G).$ In this article, we
establish a relationship between distance Seidel eigenvalues of a graph with
its distance and adjacency eigenvalues. We characterize all the connected
graphs with $\partial_{1}^{S}(G)= 3.$ Also, we determine different bounds for
the distance Seidel spectral radius and distance Seidel energy. We study the
distance Seidel energy change of the complete bipartite graph due to the
deletion of an edge. Moreover, we obtain the distance Seidel spectra of
different graph operations such as join, cartesian product, lexicographic
product, and unary operations like the double graph and extended double cover
graph. We give various families of distance Seidel cospectral and distance
Seidel integral graphs as an application.
