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等能量树的新判定方法
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Abstract:
设G和G'是一对非同谱图，当它们的特征值不能用根式表达的时候，证明它们等能量是一个非常具有挑战性的问题。但是对于树而言，此问题可借助韦达定理将其转换为证明一个代数方程有唯一的正实根。
Let G and G' be a pair of noncospectral graphs. It is a challenge problem to prove G and G' are equienergetic when their eigenvalues cannot be expressed in radicals. But for trees, this problem can be deduced to proving a specific algebraic equation with a positive root by Vieta’s theorem.
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