some relations between the distinguishing and some graph parameters

The distinguishing number of a simple graph $g$ is the least number $d(g)$ of colors needed for a coloring of $g$ which is preserved only by the identity automorphism. ##similar parameters have been defined whose concern is breaking the symmetries of a graph. ##in this paper, we present interesting connections between these parameters and some other graph parameters such as the independence number. in particular, we study conditions under which a given graph $g$ is $(d,alpha)$-ordinary, that is, for which $d(g)leq alpha(g)$.