Hacettepe Journal of Mathematics and Statistics, cilt.43, sa.6, ss.943-951, 2014 (SCI-Expanded)
AnyfinitedimensionalsemisimplealgebraAoverafieldKisisomorphictoadirectsumoffinitedimensionalfullmatrixringsoversuitabledivisionrings.Weshallconsiderthedirectsumoffinitedimensionalfullmatrixringsoverafield K. AllsuchfinitedimensionalsemisimplealgebrasariseasfinitedimensionalLeavittpathalgebras.Forthisspecificfinitedimensionalsemisimplealgebra A overafield K, wedefineauniquelydeterminedspecificgraph-calledatruncatedtreeassociatedwith A -whoseLeavittpathalgebraisisomorphicto A .Wedefineanalgebraicinvariant κ( A ) for A andcountthenumberofisomorphismclassesofLeavittpathalgebraswiththesamefixedvalueof κ(A ).Moreover,wefindthemaximumandtheminimum K-dimensionsoftheLeavittpathalgebrasofpossibletreeswithagivennumberofverticesandwealsodeterminethenumberofdistinctLeavittpathalgebrasoflinegraphswithagivennumberofvertices.