A simple proof of the spectral excess theorem for distance-regular graphs

作者：Fiol M A^*; Gago S; Garriga E

来源：Linear Algebra and Its Applications, 2010, 432(9): 2418-2422.

DOI：10.1016/j.laa.2009.07.030

• Distance-regular graph
• Adjacency matrix
• Spectrum
• Predistance polynomials
• Excess

The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Gamma with d + 1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each of its vertices. The original approach, due to Fiol and Garriga in 1997, was obtained by using a local approach, so giving a characterization of the so-called pseudo-distance-regularity around a vertex. In this paper we present a new simple projection method based in a global point of view, and where the mean excess plays an essential role.

• 出版日期2010-4-15