  Dual Seidel switching is a graph operation introduced by W.~Haemers in 1984.
This operation can change the graph, however it does not change its bipartite
double, and because of this, the operation leaves the squares of the
eigenvalues invariant. Thus, if a graph is integral then it is still integral
after dual Seidel switching. In this paper two new infinite families of
integral graphs are obtained by applying dual Seidel switching to the Star
graphs and the Odd graphs. In particular, three new $4$-regular integral graphs
with their spectra are found.

Combinatorics