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The Integer Domination Root Conjecture

Combinatorics · posed by S. Akbari, S. Alikhani, M. R. Oboudi, Y.-H. Peng, 2010 · disproved

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Statement

Akbari, Alikhani, Oboudi and Peng conjectured in 2010 that 0 and -2 are the only integer roots of the domination polynomial D(G,x)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=−4x = -4, built from an S-unit branch cancellation mechanism.

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  1. construction · #1

    Saeid Alikhani and Max Griswold, using Claude Fable 5

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    ai co developed
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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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