Cycles and Paths in Jacobson Graphs

A. Azimi1, M. Farrokhi D. G.2
1Department of Pure Mathematics, Ferpowsi University of Mashhad, Mash-Had, Iran.
2Department of Pure Mathematics, Ferdowsi University of Mashhad, Mash-Had, Iran.

Abstract

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.