In this article, the author interpolate prolific notion of co $bT^{\mu}$ graph and co $bT^{\mu}$ urysohn space by utilizing  the concept of bT$^{\mu}$ set connected functions in supra topological spaces.

Keywords: $bT^{\mu}$-set connected function, co $bT^{\mu}$ graph, co $bT^{\mu}$ urysohn space.