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Graph energy monotonicity conjecture disproven for all p >= 1

By PulseAugur Editorial · [1 sources] ·

Researchers Guo, Tang, Liu, and Wang have disproven a conjecture regarding the positive p-energy of graphs. The conjecture, initially proposed by Guo in 2021, suggested that positive square energy should exhibit edge-addition monotonicity, similar to the spectral radius. While this was shown to fail for p=2, a subsequent preprint by Tang, Liu, and Wang conjectured monotonicity for p >= 3. The current work demonstrates that for any real p > 2, there exist graphs where adding an edge decreases the positive p-energy, thus refuting the extended conjecture. AI

RANK_REASON Academic paper presenting a mathematical proof that disproves a conjecture. [lever_c_demoted from research: ic=1 ai=0.1]

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Graph energy monotonicity conjecture disproven for all p >= 1

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Academic paper presenting a mathematical proof that disproves a conjecture. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv cs.AI TIER_1 English(EN) · Koyar Afrasyab ·

    Edge-addition monotonicity of positive p-energy fails for every p >= 1

    arXiv:2609.13476v1 Announce Type: cross Abstract: At a 2021 AIM workshop, Guo conjectured that the positive square energy s+ = E+_2 should inherit the familiar edge-addition monotonicity of the spectral radius, rho(G + uv) >= rho(G). That conjecture was subsequently shown to fail…

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