Talk by Chris Godsil.
Physicists are interested in "graphs with tails"; these are constructed by choosing a graph X and a subset C of its vertices, then attaching a path of length n to each vertex in C. We ask what is the spectrum of such graph? What happens if n increases? We will see that the answer reduces to questions about the matrix
M(ζ) := (ζ_ζ^{-1})I - A -ζ D
where D is the diagonal 01-matrix with D_{i,i} = 1 if i is in C. (For physicists, the block of M(ζ)^{-1} indexed by the entries of C determines the so-called scattering matrix of a quantum system, but we won't go there.)
A path is built by chaining copies of K_2 together. We consider what happen if we use some other graph in place of K_2.
