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  "body": "\n## Definition\n\nLet $Q$ be a finite [[quiver|RE9YFFS3TS]].\nThe *underlying graph* of $Q$ is the graph with vertex set $Q_0$ and one undirected edge between $s(a)$ and $t(a)$ for each arrow $a \\in Q_1$.\nThe quiver $Q$ is a *Dynkin quiver* if its underlying graph is one of the simply laced Dynkin diagrams:\n\n1. $A_n$ for $n \\ge 1$, a path with $n$ vertices;\n2. $D_n$ for $n \\ge 4$, a path with $n - 2$ vertices and two extra vertices joined to one end vertex;\n3. $E_6$, $E_7$ or $E_8$, a path with $n - 1$ vertices and one extra vertex joined to the third vertex from one end, for $n = 6, 7, 8$.\n\n## Remarks\n\nExample: $1 \\to 2 \\leftarrow 3$ is a Dynkin quiver, since its underlying graph is the path with $3$ vertices, of type $A_3$.\nNon-example: the Kronecker quiver, with two arrows $1 \\to 2$, is not Dynkin, since its underlying graph has a double edge.\nNon-example: a quiver with a loop, or whose underlying graph is a cycle, is not Dynkin.\nA Dynkin quiver is connected and has no oriented cycles, and every orientation of a Dynkin diagram is a Dynkin quiver.\n",
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