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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)

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)

Traditional use of noncultivated vegetables has decreased with the development of agriculture and global supply chains. However, some species are still consumed as part of our traditional Mediterranean diet. Plants are among the most important sources of natural antioxidants for retarding lipid oxidative rancidity in foods or for pharmaceutical applications… (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)

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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