  This paper is concerned with the structures introduced recently by the
authors of the current paper concerning the multiplier Hopf $*$-graph algebras
and also the Cuntz-Krieger algebras and their relations with the $C^*$-graph
algebras, and once again by using the $C^*$-graph algebra constructions
associated to our toy example, to initiate our first class of examples
concerning the multiplier Hopf $*$-graph algebras.
  At the final part of the paper, we apply our study to the $SL(n)$ case over
the field of complex numbers, and prove that $(\mathcal{O}(SL(n),\Delta)$
possesses the initial requirements of being a discrete quantum group in the
sense of Van Daele, and propose a direction in approaching one step further to
the problem raised by Wang, asking ``if finite groups of Lie type have an
analogue of $q$-deformations into finite quantum groups?''.
