Geodesic
Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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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 defined from the spectrum of a graph, one of these families is the system of the predistance polynomials which, in the case of distance-regular graphs, turns out to be the sequence of distance polynomials. The applications range from (quasi-spectral) characterizations of distance-regular graphs, walk-regular graphs, local distance-regularity and completely regular codes, to some results on representation theory.
DOI : 10.37236/172
Classification : 05C12, 05C50, 05E30
Mots-clés : distance-regularity in graphs 
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     title = {Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes},
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     year = {2009},
     volume = {16},
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M. Cámara; J. Fàbrega; M. A. Fiol; E. Garriga. Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/172

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