English(EN) Edge-addition monotonicity of positive p-energy fails for every p >= 1

图能量单调性猜想对所有p>=1均被证伪

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-15 04:00

研究人员Guo、Tang、Liu和Wang已经证伪了关于图的正p能量的一个猜想。该猜想最初由Guo于2021年提出，认为正平方能量应该像谱半径一样表现出边添加单调性。虽然这已被证明对p=2失效，但Tang、Liu和Wang随后的一篇预印本猜想对于p>=3也存在单调性。目前的工作表明，对于任何实数p>2，都存在这样的图，添加一条边会降低其正p能量，从而反驳了扩展猜想。 AI

排序理由学术论文，提出数学证明证伪一个猜想。[lever_c_demoted from research: ic=1 ai=0.1]

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arXiv cs.AI TIER_1 English(EN) · Koyar Afrasyab · 2026-09-15 04:00

对于每一个 p >= 1，正 p-能量的边缘添加单调性都失效

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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对于每一个 p >= 1，正 p-能量的边缘添加单调性都失效

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