Defining a Zeroth Homotopy Invariant for Graphs

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

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. Retrieved from https://journals.calstate.edu/pump/article/view/2250