Defining a Zeroth Homotopy Invariant for Graphs
Keywords:
graph; graph product; functor; connected component
Abstract
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.
Published
2020-02-19
How to Cite
Kane, C., Novoa, D., Scull, L., & Thompson, J. (2020). Defining a Zeroth Homotopy Invariant for Graphs. The PUMP Journal of Undergraduate Research, 3, 37-51. https://doi.org/10.46787/pump.v3i0.2250
Section
Articles
Copyright (c) 2020 Coleman Kane, Diego Novoa, Laura Scull, Jonathon Thompson
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