Defining a Zeroth Homotopy Invariant for Graphs

Authors

  • Coleman Kane Fort Lewis College
  • Diego Novoa Fort Lewis College
  • Laura Scull Fort Lewis College
  • Jonathon Thompson Fort Lewis College

DOI:

https://doi.org/10.46787/pump.v3i0.2250

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.

Author Biographies

Coleman Kane, Fort Lewis College

Mathematics major at Fort Lewis College.  Graduated in Spring 2019.  

Diego Novoa, Fort Lewis College

Chemistry major at Fort Lewis College.  Graduated Spring 2019. 

Laura Scull, Fort Lewis College

Professor, Department of Mathematics, Fort Lewis College.  

Jonathon Thompson, Fort Lewis College

Mathematics Major at Fort Lewis College.  Not graduated but not currently enrolled.  

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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

Issue

Vol. 3 (2020): PUMP Journal of Undergraduate Research

Section

Articles

License

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.