Sparse topologies with small spectrum size
Robert Elsässer⋆, Rastislav Kráľovič, Burkhard Monien · Theoretical Computer Science · 2003
One of the fundamental properties of a graph is the number of distinct eigenvalues of its adjacency or Laplace matrix. Determining this number is of theoretical interest as well as of practical impact. Sparse graphs with small spectra exhibit excellent structural properties and can act as interconnection topologies. In this paper, for any n we present graphs, for which the product of their vertex degree and the number of different eigenvalues is small. It is known that load balancing can be performed on such graphs in a small number of steps.