  Any finite dimensional semisimple algebra A over a field K is isomorphic to a
direct sum of finite dimensional full matrix rings over suitable division
rings. In this paper we will consider the special case where all division rings
are exactly the field K. All such finite dimensional semisimple algebras arise
as a finite dimensional Leavitt path algebra. For this specific finite
dimensional semisimple algebra A over a field K, we define a uniquely detemined
specific graph - which we name as a truncated tree associated with A - whose
Leavitt path algebra is isomorphic to A. We define an algebraic invariant
{\kappa}(A) for A and count the number of isomorphism classes of Leavitt path
algebras with {\kappa}(A)=n. Moreover, we find the maximum and the minimum
K-dimensions of the Leavitt path algebras of possible trees with a given number
of vertices and determine the number of distinct Leavitt path algebras of a
line graph with a given number of vertices.
