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Tiling of Prime and Composite Kirchhoff Graphs Public

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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.
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Identifier
  • 49661
  • E-project-030422-205938
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Year
  • 2022
Date created
  • 2022-03-04
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