Spectral bounds and distance-regularity

Abstract: This is a survey of recent results showing that the usual concepts of (local or global) distance-regularity in a graph can be thought of as an extremal (numeric) property of the graph. This is because such structures appear when a certain spectral bound is attained, so yielding striking characterizations of distance-regularity, with the peculiarity of involving only numerical (instead of the usual matricial) identities. Other results providing bounds for specific parameters of the graph, such as its eigenvalue multiplicities, are also derived. [Copyright &y& Elsevier]