Graduation Year


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science



Reader 1

Francis Edward Su

Reader 2

Dagan Karp

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2020 Savana Jade Ammons


In this thesis, we develop a discrete analogue to the Poincaré–Hopf Theorem. We define the notion of a vector field on a graph, and establish an index theory for such a field. Specifically, we create well-defined indices for the nodes and “cells" formed by a planar graph. Then, we show that the sum of these indices remains constant for certain types of planar graphs, regardless of the discrete vector fields they have.