【摘要】 设图G是简单连通图.如果任何一个与图G关于拉普拉斯矩阵同谱的图,都与图G同构,称图G可由其拉普拉斯谱确定.定义了树Y_n和树F(2,n,1)两类特殊结构的树.利用同谱图线图的特点,证明了树Y_n和树F(2,n,1)可由其拉普拉斯谱确定.更多还原

【Abstract】 Let G be a simple connected graph.A graph G is called to be determined by its Laplacian spectrum if any graph having the same Laplacian spectrum as G is isomorphic to G.In this paper,tree Y_n and tree F(2,n,1) which have special structures are defined.It is proved that these two families of trees are determined by their Laplacian spectrum,considering the properties of the line graphs of the cospectral graphs.更多还原