  It is known that complete multipartite graphs are determined by their
distance spectrum but not by their adjacency spectrum. The Seidel spectrum of a
graph $G$ on more than one vertex does not determine the graph, since any graph
obtained from $G$ by Seidel switching has the same Seidel spectrum. We consider
$G$ to be determined by its Seidel spectrum, up to switching, if any graph with
the same spectrum is switching equivalent to a graph isomorphic to $G$. It is
shown that any graph which has the same spectrum as a complete $k$-partite
graph is switching equivalent to a complete $k$-partite graph, and if the
different partition sets sizes are $p_1,\ldots, p_l$, and there are at least
three partition sets of each size $p_i$, $i=1,\ldots, l$, then $G$ is
determined, up to switching, by its Seidel spectrum. Sufficient conditions for
a complete tripartite graph to be determined by its Seidel spectrum are
discussed, and a conjecture is made on complete tripartite graphs on more than
18 vertices.
