Defining a Zeroth Homotopy Invariant for Graphs - Kane, Coleman; Novoa, Diego; Scull, Laura; Thompson, Jonathon (The PUMP Journal of Undergraduate Research, 2020)
We define a zeroth homotopy π0(G) for a graph G. Our definition is a variation on the usual set of connected components and has the structure of a graph, and not just a set. We prove that our π0 is functorial and respects products: π0(G x H) ≅ π0(G) x π0(H), a property that the set of components fails to have.