Central exponent of algebras with graded involution

The asymptotic behavior of central codimensions has been studied for ordinary algebras, [Formula: see text]-algebras and G-graded algebras with G a finite abelian group. In this paper, we study central [Formula: see text]-polynomials of finite-dimensional superalgebras with graded involution which form a particular class of algebras with a generalized H-action. We are able to prove the existence and the integrality of a limit called the central [Formula: see text]-graded exponent that gives a quantitative measure of the growth of the central [Formula: see text]-polynomials.