@article{Kane_Novoa_Scull_Thompson_2020, title={Defining a Zeroth Homotopy Invariant for Graphs}, volume={3}, url={https://journals.calstate.edu/pump/article/view/2250}, abstractNote={<p>We define a zeroth homotopy π<sub>0</sub>(<em>G</em>) for a graph <em>G</em>. 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 π<sub>0</sub> is functorial and respects products: π<sub>0</sub>(<em>G x H</em>) ≅ π<sub>0</sub>(<em>G</em>) <em>x</em> π<sub>0</sub>(<em>H</em>), a property that the set of components fails to have.</p>}, journal={The PUMP Journal of Undergraduate Research}, author={Kane, Coleman and Novoa, Diego and Scull, Laura and Thompson, Jonathon}, year={2020}, month={Feb.}, pages={37-51} }