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Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes
Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Fàbrega Canudas, José; Cámara Vallejo, Marc
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Orthogonal polynomials
Graph theory
Discrete variable
Graphs
Completely regular codes
Local spectrum
Distance regularity
Polinomis ortogonals
Grafs, Teoria de
Classificació AMS::05 Combinatorics::05C Graph theory
Attribution-NoDerivs 3.0 Unported
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