Cycles and paths in Jacobson graphs
  All finite Jacobson graphs with a Hamiltonian cycle or path, or Eulerian tour or trail are determined, and it is shown that a finite Jacobson graph is Hamiltonian if and only if it is pancyclic. Also, the length of the longest induced cycles and paths in finite Jacobson graphs are obtained. 
Ali Azimi and Mohammad Farrokhi Derakhshandeh Ghouchan
math.AC