%0 Journal Article %1 Fiol12 %A Fiol, M. A. %A Gago, S. %A Garriga, E. %D 2010 %J Linear Algebra and its Applications %K distance-regular graph.theory polynomial predistance spectral.excess %N 9 %P 2418 - 2422 %R 10.1016/j.laa.2009.07.030 %T A Simple Proof of the Spectral Excess Theorem for Distance-Regular Graphs %V 432 %X The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ 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.

@article{Fiol12, abstract = {The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ 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. }, added-at = {2014-01-10T21:28:21.000+0100}, author = {Fiol, M. A. and Gago, S. and Garriga, E.}, biburl = {https://www.bibsonomy.org/bibtex/2cb6c1ff7ffe471c0ddccbb8d73743a37/ytyoun}, doi = {10.1016/j.laa.2009.07.030}, interhash = {ee5165ff049926b5e3f53bc72c73529a}, intrahash = {cb6c1ff7ffe471c0ddccbb8d73743a37}, issn = {0024-3795}, journal = {Linear Algebra and its Applications }, keywords = {distance-regular graph.theory polynomial predistance spectral.excess}, note = {Special Issue devoted to Selected Papers presented at the Workshop on Spectral Graph Theory with Applications on Computer Science, Combinatorial Optimization and Chemistry (Rio de Janeiro, 2008) }, number = 9, pages = {2418 - 2422}, timestamp = {2017-11-22T06:56:44.000+0100}, title = {A Simple Proof of the Spectral Excess Theorem for Distance-Regular Graphs }, volume = 432, year = 2010 }