  A distinguishing $r$-labeling of a digraph $G$ is a mapping $\lambda$ from
the set of verticesof $G$ to the set of labels $\{1,\dots,r\}$ such that no
nontrivial automorphism of $G$ preserves all the labels.The distinguishing
number $D(G)$ of $G$ is then the smallest $r$ for which $G$ admits a
distinguishing $r$-labeling.From a result of Gluck (David Gluck, Trivial
set-stabilizers in finite permutation groups,{\em Can. J. Math.} 35(1) (1983),
59--67),it follows that $D(T)=2$ for every cyclic tournament~$T$ of (odd) order
$2q+1\ge 3$.Let $V(T)=\{0,\dots,2q\}$ for every such tournament.Albertson and
Collins conjectured in 1999that the canonical 2-labeling $\lambda^*$ given
by$\lambda^*(i)=1$ if and only if $i\le q$ is distinguishing.We prove that
whenever one of the subtournaments of $T$ induced by vertices $\{0,\dots,q\}$or
$\{q+1,\dots,2q\}$ is rigid, $T$ satisfies Albertson-Collins Conjecture.Using
this property, we prove that several classes of cyclic tournaments satisfy
Albertson-Collins Conjecture.Moreover, we also prove that every Paley
tournament satisfies Albertson-Collins Conjecture.
