  The paper contains a proof of the conjecture of M. Klin and D.
Maru$\breve{\rm s}$i$\breve{\rm c}$ that an automorphism group of a transitive
graph contains a permutation, decomposed in cycles of the same length. The
proof is based on the $k$-orbit theory developed by author.
  Key words: $k$-orbits, partitions, permutations, symmetry, groups
