The characteristic polynomial of ladder digraph and an annihilating uniqueness theorem Original Research Article

Let G be a digraph with n vertices and A(G) be its adjacency matrix. A monic polynomial f(x) of degree at most n is called an annihilating polynomial of G if f (A(G)) = 0. G is said to be annihilatingly unique if it possesses a unique annihilating polynomial. In this paper, we give the explicit expression for the characteristic polynomial of the ladder digraph and show that the ladder digraph is annihilatingly unique.