... thing The Proper and Adjacency Polynomials In this section we introduce two orthogonal systems of polynomials and, after recalling their main properties, we study some of their (old and new) applications ... investigate some new applications of these polynomials, deriving new bounds for the radius of a graph and the “weight k-excess” of a vertex Generalizing these results, and grouping ideas of Van Dam ... of the former) where Vk = Γk (u); and that, as suggested by the notation, such polynomials coincide, in fact, with the proper polynomials In addition, using property (c.2) and the adjacency polynomials...