| 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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