On the algebraic theory of pseudo-distance-regulariry around a set
Tipo de documentoArtículo
Fecha de publicación1999-09
Condiciones de accesoAcceso restringido por política de la editorial
Let C be a connected graph with vertex set V, adjacency matrix A, positive eigenvector and corresponding eigenvalue 0. A natural generalization of distance-regularity around a vertex subset C V , which makes sense even with non-regular graphs, is studied. This new concept is called pseudo-distance-regularity, and its definition is based on giving to each vertex u 2 V a weight which equals the corresponding entry u of and “regularizes” the graph. This approach reveals a kind of central symmetry which, in fact, is an inherent property of all kinds of distance-regularity, because of the distance partition of V they come from. We come across such a concept via an orthogonal sequence of polynomials, constructed from the “local spectrum” of C, called the adjacency polynomials because their definition strongly relies on the adjacency matrix A. In particular, it is shown that C is “tight” (that is, the corresponding adjacency polynomials attain their maxima at 0) if and only if C is pseudo-distance-regular around C. As an application, some new spectral characterizations of distance-regularity around a set and completely regular codes are given.
CitaciónFiol, M. A.; Garriga, E. On the algebraic theory of pseudo-distance-regulariry around a set. "Linear algebra and its applications", Setembre 1999, vol. 298, p. 115-141.
Versión del editorhttp://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V0R-3YC0J0W-T&_user=1517299&_coverDate=09%2F01%2F1999&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_acct=C000053450&_version=1&_urlVersion=0&_userid=1517299&md5=183617b4ec220701db7392169edaf434&searchtype=a
|Ps-dis-reg-C (LAA 1999).pdf||Article principal||215.7Kb||Acceso restringido|