缅北强奸

Matching Polynomials of Covers of Graphs.

Given a connected undirected graph G there is a notion of a cover H of G and degree of the cover. 聽If G is finite, there are finitely many covers of fixed degree d, and one can form interesting averages over the family of such covers. For example, the average matching polynomial M_H(T) is something we call a d-matchings polynomial M_{d,G}(T). 聽The same polynomial arises when one averages the `new part' of the characteristic polynomial of the adjacency matrix A(H) for covers of degree *d+1*. 聽We will elaborate on these points and discuss interesting number-theoretic properties possessed by M_{d,G}(T). 聽If time permits, we will mention some open problems and also indicate other averages one might consider.