A Kirchhoff graph is a vector graph with orthogonal cycles and vertex cuts. We present an algorithm that constructs all the Kirchhoff graphs up to a fixed edge multiplicity. We explore the tiling of prime Kirchhoff graphs. Specifically, we show the existence of countably infinitely many prime Kirchhoff graphs given a set of initial fundamental Kirchhoff graphs. We also explore the minimal multiplicity for which nontrivial Kirchhoff graphs exist.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Wang, Jessica

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-030422-205938
• 49661

Keyword

• Graph Theory
• Kirchhoff Graph
• Mathematical Sciences

Advisor

• Fehribach, Joseph D.

Year

• 2022

Date created

• 2022-03-04

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright