The Distinguishing Chromatic Number of the Graph, C_n ◦ I_m

In this paper, we will extend the works of Collins and Trenk, by finding the distinguishing chromatic number of the graph C_n ◦ I_m, n, m ∈ N. We will first look at a couple of examples, starting with m = 2, and providing a theorem for C_n ◦ I_2 , while also offering an example of a coloring scheme for each n and explaining why the scheme works. We will then look at the case for m = 3, followed by the general case.