Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes
Tipus de documentArticle
Data publicació2000-08
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Reconeixement-SenseObraDerivada 3.0 Genèrica
Abstract
We present some related families of orthogonal polynomials of a discrete variable
and survey some of their applications in the study of (distance-regular) graphs and
(completely regular) codes. One of the main peculiarities of such orthogonal systems
is their non-standard normalization condition, requiring that the square norm of each
polynomial must equal its value at a given point of the mesh. For instance, when they
are de¯ned from the spectrum of a graph, one of these families is the system of the pre-
distance polinomials which, in the case of distance-regular graphs, turns out to be the
sequence of distance polinomials. The applications range from (quasi-spectral) char-
acterizations of distance-regular graphs, walk-regular graphs, local distance-regularity
and completely regular codes, to some results on representation theory.
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