Date of Submission

Spring 2011

Academic Program

Mathematics

Advisor

Lauren Rose

Abstract/Artist's Statement

Gross and Tucker’s voltage graph construction assigns group elements as weights to the edges of an oriented graph. This construction provides a blueprint for inducing graph covers. Thomas Zaslavsky studies the criteria for balance in voltage graphs. This project primarily examines the relationship between the group structure of the set of all possible assignments of a group to a graph, including the balanced subgroup, and the isomorphism classes of covering graphs. We examine connectedness, planarity, and chromatic number in the derived graph. Lastly we explain the future research possibilities involving the fundamental group.

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