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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… (More)

Given a simple connected graph Γ 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. We then say that C is a completely pseudo-regular code. Up to now, most of the characterizations of pseudo-distance-regularity has been derived from a combinatorial… (More)

- M. C. Sánchez-Mata, R. D. Cabrera Loera, P. Morales, V. Fernández-Ruiz, M. Cámara, C. Díez Marqués +2 others
- Genetic Resources and Crop Evolution
- 2011

The intake of traditionally consumed wild edible species is nowadays receiving renewed attention, due to the recognition of their potential benefits for human health. This paper represents a contribution to the knowledge of the chemical composition of different wild and under-utilized vegetables of the Mediterranean area, concerning their organic acid… (More)

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… (More)

A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if… (More)

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