The endomorphism monoid of

In this paper, the endomorphism monoid of P n ¯ , the complement of a path P n with n vertices, is explored explicitly. It is shown that End ( P n ¯ ) is orthodox. Some enumerative problems concerning End ( P n ¯ ) are solved. In particular, the endomorphism spectrum and the endomorphism type of P n ¯ are given.