Graphs emerging from the solutions to the periodic discrete Toda equation over finite fields
Masataka Kanki, Yuki Takahashi, Tetsuji Tokihiro · Nonlinear Theory and Its Applications IEICE · 2016
The periodic discrete Toda equation defined over finite fields has been studied. We obtained the finite graph structures constructed by the network of states where edges denote possible time evolutions. We simplify the graphs by introducing a equivalence class of cyclic permutations to the initial values. We proved that the graphs are bi-directional and that they are composed of several arrays of complete graphs connected at one of their vertices. The condition for the graphs to be bi-directional is studied for general discrete equations.MSC2010: 37K10, 37P05, 37P25, 37J35