2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74518The 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, groups7 pages, Latex2eGeneral MathematicsCombinatorics20C99, 20B05text