... trivial.) Then, by the converse of Theorem 2.5, it must be Qku≥ 1. On the other hand, in the proof of Theorem the electronic journal of combinatorics 4 (1997), #R21 3 In the rest of this introductory ... on the spectrum of the graph [17] . Afterwards, we further investigate some new applications of these polynomials, deriving new bounds for the radius of a graph and the “weight k-excess” of a ... following Godsil [24] , we say that the graph Γiis the i-th class of the scheme, and so we indistinctly use the words graph or“class” to mean the same thing.2 The Proper and Adjacency Polynomials In...