Abstract: Since 1986 (SIAM International Conference on Parallel Processing), Cayley graphs are used as a "tool to construct vertex-symmetric interconnection networks." In 2009, O. Ahmadi, N. Alon, I.F. Blake, and I.E. Shparlinski studied graphs with integral spectrum, i.e.whose eigenvalues are integers. It was shown that the most graphs have nonintegral eigenvalues. On the other hand, it was noted that integral graphs play an important role in quantum networks supporting the so-called perfect state transfer. In this talk we discuss recent results on integral networks presented by Cayley graphs over the symmetric group.

Cite: Konstantinova E.V.
Integral networks
The 13th International Conference on Network Analysis 10-12 May 2023