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A simple proof of the spectral excess theorem for distance-regular graphs
- Source :
-
Linear Algebra & its Applications . Apr2010, Vol. 432 Issue 9, p2418-2422. 5p. - Publication Year :
- 2010
-
Abstract
- Abstract: The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph with distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance ) 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 432
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 48406794
- Full Text :
- https://doi.org/10.1016/j.laa.2009.07.030