On the local spectra of the subconstituents of a vertex set and completely pseudo-regular codes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Oct 2014Embargo end date: 01 Jan 2012 Spain English Publisher:Elsevier BVJournal:Discrete Applied Mathematics, volume 176, pages 12-18 (issn: 0166-218X,

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Authors: Cámara Vallejo, Marc; Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest;

doi: 10.1016/j.dam.2013.09.018 , 10.48550/arxiv.1212.3815

arXiv: 1212.3815

handle: 2117/24667

On the local spectra of the subconstituents of a vertex set and completely pseudo-regular codes

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Abstract

The local spectrum of a vertex set in a graph has been proven to be very useful to study some of its metric properties. It also has applications in the area of pseudo-distance-regularity around a set and can be used to obtain quasi-spectral characterizations of completely (pseudo-)regular codes. In this paper we study the relation between the local spectrum of a vertex set and the local spectrum of each of its subconstituents. Moreover, we obtain a new characterization for completely pseudo-regular codes, and consequently for completely regular codes, in terms of the relation between the local spectrum of an extremal set of vertices and the local spectrum of its antipodal set. We also present a new proof of the version of the Spectral Excess Theorem for extremal sets of vertices.

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Spain

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Keywords

:Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis [Àrees temàtiques de la UPC], pseudo-distance-regularity, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis, Polynomials, Local spectrum, Subconstituents, 11C Polinomis i matrius, GRAPHS, POLYNOMIALS, local spectrum, Predistance polynomials, FOS: Mathematics, Mathematics - Combinatorics, subconstituents, Extremal problems in graph theory, predistance polynomials, Graphs and linear algebra (matrices, eigenvalues, etc.), Completely regular code, completely regular code, 05C50, 05E30, Polinomis, Combinatorics (math.CO), Pseudo-distance-regularity

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