  We consider a class $G(S^n)$ of orientation preserving Morse-Smale
diffeomorphisms of the sphere $S^{n}$ of dimension $n>3$ in assumption that
invariant manifolds of different saddle periodic points have no intersection.
We put in a correspondence for every diffeomorphism $f\in G(S^n)$ a colored
graph $\Gamma_f$ enriched by an automorphism $P_f$. Then we define the notion
of isomorphism between two colored graphs and prove that two diffeomorphisms
$f, f'\in G(S^n)$ are topologically conjugated iff the graphs $\Gamma_f$,
$\Gamma_f'$ are isomorphic. Moreover we establish the existence of a
linear-time algorithm for distinguishing two colored graphs of diffeomorphisms
from the class $G(S^n)$.
