Pith. sign in

REVIEW

Prime, composite and fundamental Kirchhoff graphs

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2207.11435 v1 pith:JPQEJX6S submitted 2022-07-23 math.CO

Prime, composite and fundamental Kirchhoff graphs

classification math.CO
keywords kirchhoffgraphsgraphprimealgorithmexistencefundamentalmultiplicity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original 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.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.