On the polynomial of a path
Linear Algebra and Its Applications
Mathematics and Computer Science
Let A(Pn) be the adjacency matrix of the path on n vertices. Suppose that r(?) is a polynomial of degree less than n, and consider the matrix M = r(A>/(Pn)). We determine all polynomials for which M is the adjacency matrix of a graph.
Beezer, R. "On the Polynomial of a Path." Linear Algebra and Its Applications. 63.1 (1984): 221-225. Print.