The study of finite semigroups is of interest because of its application inseveral branches of science, for instance, its uses and advantages in mathematics, computer science and finite machines are well-known. The power graph associated to such semigroups is also an applicable tool in demonstrating the properties of semigroups. The completeness and Eulerianity of power graphs associated to finite commutative semigroups and finite non-commutative epigroups are studied in this paper. We show that these graphs may be non-complete for the monogenic semigroups and we gives a necessaryand sufficient condition for such graphs to be complete when finite regular epigroups are considered. This study answers in part the natural question”Is there any non-isomorphic non-group semigroups with the same complete power graph?” تفاصيل المقالة