The endomorphism monoid of \(\overline{P_n}\). (Q925021)

Let \(\overline{P_n}\) be the complement of the path \(P_n\) with \(n\) vertices (all graphs are finite undirected without loops and multiple edges). It is proved that the endomorphism monoid of \(\overline{P_n}\) is orthodox. The number of elements in \(\text{End}(\overline{P_n})\) and the endomorphism spectrum, i.e., the number of endomorphisms of a particular type (half-strong, locally strong, quasi-strong, strong endomorphisms and automorphisms) are also found.