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{\bf Harm Derksen and Theodore Owen}
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{\bf New Graphs of Finite Mutation Type}
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To a directed graph without loops or $2$-cycles, we can associate a
skew-symmetric matrix with integer entries.  Mutations of such
skew-symmetric matrices, and more generally skew-symmetrizable
matrices, have been defined in the context of cluster algebras by
Fomin and Zelevinsky.  The mutation class of a graph $\Gamma$ is the
set of all isomorphism classes of graphs that can be obtained from
$\Gamma$ by a sequence of mutations.  A graph is called
mutation-finite if its mutation class is finite.  Fomin, Shapiro and
Thurston constructed mutation-finite graphs from triangulations of
oriented bordered surfaces with marked points. We will call such
graphs ``of geometric type''. Besides graphs with $2$ vertices, and
graphs of geometric type, there are only 9 other ``exceptional''
mutation classes that are known to be finite. In this paper we
introduce 2 new exceptional finite mutation classes.



\bye