The Integer Domination Root Conjecture
Statement
Akbari, Alikhani, Oboudi and Peng conjectured in 2010 that 0 and -2 are the only integer roots of the domination polynomial , 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 , built from an S-unit branch cancellation mechanism.
Context
A 2010 specialist conjecture with a genuine partial-results literature (trees, unicyclic graphs, exhaustive small-order checks).
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"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.
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