A Simple Proof of the Spectral Excess Theorem for Distance-Regular Graphs
M. Fiol, S. Gago, and E. Garriga. Linear Algebra and its Applications, 432 (9):
2418 - 2422(2010)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).
DOI: 10.1016/j.laa.2009.07.030
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.
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)
%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
}