距离正则图的Laplacian谱过剩定理
The Laplacian spectral excess theorem for distance-regular graphs
摘要：
谱过剩定理指出，在一个正则图G中，平均过剩数，即距离顶点最大距离处顶点数的平均值，上界于谱过剩数（一个由G的邻接谱计算的数），并且G是距离正则的当且仅当等式成立。本文在不要求G的正则性的情况下，利用Laplacian谱证明了相应的结果。
英文摘要：
The spectral excess theorem states that, in a regular graph G, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above by the spectral excess (a number that is computed by using the adjacency spectrum of G), and G is distance-regular if and only if equality holds. In this note we prove the corresponding result by using the Laplacian spectrum without requiring regularity of G.
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