The characteristic polynomial of ladder digraph and an annihilating uniqueness theorem (Q1916390)

Suppose \(A(G)\) is an adjacency matrix of digraph \(G\) and \(G\) has \(n\) vertices. If \(f(x)\) is a monic polynomial of degree at most \(n\), and \(f(A(G)) = 0\), then \(f(x)\) is an annihilating polynomial of \(G\). The authors give the explicit expression for the characteristic polynomial of a ladder digraph and establish that the ladder digraph has a unique annihilating polynomial.