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Títol: Combinatorial vs. algebraic characterizations of pseudo-distance-regularity around a set
Autor: Cámara Vallejo, Marc
Fàbrega Canudas, José
Fiol Mora, Miquel Àngel
Garriga Valle, Ernest
Altres autors/autores: Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
Matèries: Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta
Graph theory
Combinatorics
Pseudo-Distance-regular graph
Adjacency matrix
Local spectrum
Orthogonal predistance polynomials
Terwilliger algebras
Completely regular code
Grafs, Teoria de
Combinacions (Matemàtica)
Classificació AMS::05 Combinatorics::05C Graph theory
Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
Tipus de document: External research report
Descripció: Given a simple connected graph $\Gamma$ and a subset of its vertices $C$, the pseudo-distance-regularity around $C$ generalizes, for not necessarily regular graphs, the notion of completely regular code. Up to now, most of the characterizations of pseudo-distance-regularity has been derived from a combinatorial definition. In this paper we propose an algebraic (Terwilliger-like) approach to this notion, showing its equivalence with the combinatorial one. This allows us to give new proofs of known results, and also to obtain new characterizations which do not depend on the so-called $C$-spectrum of $\Gamma$, but only on the positive eigenvector of its adjacency matrix. In the way, we also obtain some results relating the local spectra of a vertex set and its antipodal. As a consequence of our study, we obtain a new characterization of a completely regular code $C$, in terms of the number of walks in $\Gamma$ with an endvertex in $C$.
Altres identificadors i accés: http://hdl.handle.net/2117/3016
Disponible al dipòsit:E-prints UPC
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