Seidel Integral Complete r-Partite Graphs

A graph is S-integral (or Seidel integral) if the spectrum of its Seidel matrix consists entirely of integers. In this paper, we give a sufficient and necessary condition for complete r-partite graphs to be S-integral, from which we construct infinitely many new classes of S-integral graphs. We also present an upper bound and a lower bound for the smallest S-eigenvalue (or Seidel eigenvalue) of a complete multipartite graph.