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The Integer Domination Root Conjecture

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.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jul 31, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: The Integer Domination Root Conjecture · Integer domination roots

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Saeid Alikhani
human · human collaborator

Max Griswold
human · human collaborator

Claude Fable 5
model · ai model contributor · Anthropic

Lineage and corrections

This event attributed to Max Griswold

This event attributed to Saeid Alikhani

This event attributed to Claude Fable 5

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