$C^{\ast }$- Colored graph algebras

Following our previous works on $C^{\ast }$-graph algebras and the associated Cuntz-Krieger graph families, in this paper we will try to have a look at the colored version of these structures and to see what a $C^{\ast }$-colored graph algebra might mean by employing some constructive examples very close to the toy example used in our previous works, and we also will try to study their graph theoretical properties as possible.