Prime, composite and fundamental Kirchhoff graphs
Combinatorics
2022-07-26 v1
Abstract
A Kirchhoff graph is a vector graph with orthogonal cycles and vertex cuts. An algorithm has been developed that constructs all the Kirchhoff graphs up to a fixed edge multiplicity. This algorithm is used to explore the structure of prime Kirchhoff graph tilings. The existence of infinitely many prime Kirchhoff graphs given a set of fundamental Kirchhoff graphs is established, as is the existence of a minimal multiplicity for Kirchhoff graphs to exist.
Keywords
Cite
@article{arxiv.2207.11435,
title = {Prime, composite and fundamental Kirchhoff graphs},
author = {Jessica Wang and Joseph Fehribach},
journal= {arXiv preprint arXiv:2207.11435},
year = {2022}
}