Koç, AytenEsin, SongülGüloğlu, İsmail ŞuayipKanuni, Müge2020-04-302020-04-3020141303-5010https://hdl.handle.net/20.500.12684/2313Kanuni, Muge/0000-0001-7436-039X;WOS: 000348691000006Any 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. We shall consider the direct sum of finite dimensional full matrix rings over a field K. All such finite dimensional semisimple algebras arise as finite dimensional Leavitt path algebras. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely determined specific graph - called 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 the same fixed value of kappa(A). 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 we also determine the number of distinct Leavitt path algebras of line graphs with a given number of vertices.eninfo:eu-repo/semantics/closedAccessFinite dimensional semisimple algebraLeavitt path algebraTruncated treesLine graphsArticle436943951WOS:000348691000006N/AQ4