Abstract: let u_n=Σ_{k ≤ nn-k}^k and P_n denote the path with n vertices. In this paper, it is proved that P_n are shown to be irreducible path if n=3 of n=q-1, where q ≥ 3 are prime and[(u_q-1-1) + 1]/u_q-1 are positive integer.

Key words: adjoint polynomial, irreducible path