Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Akbari, Alikhani, Oboudi and Peng conjectured in 2010 that 0 and -2 are the only integer roots of the domination polynomial $D(G, x)$, proven for trees and unicyclic graphs and verified exhaustively for small orders. The paper gives a counterexample of order 33 with an integer domination root at $x = -4$, built from an S-unit branch cancellation mechanism.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
"The concept and theoretical formulation of the S-Unit Branch Cancellation mechanism were generated by Claude Fable 5." The authors verified all formal proofs and carried out independent computational validations. Alikhani is one of the conjecture's original posers.
Provider: Anthropic · Prompt public: unknown · Independence: unknown
Author-verified by exact enumeration, and one author co-posed the conjecture being refuted; no external review yet.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.