  Let E be an arbitrary graph, K be any field and let L be the corresponding
Leavitt path algebra. Necessary and sufficient conditions (which are both
algebraic and graphical) are given under which all the irreducible
representations of L are finitely presented. In this case, the graph E turns
out to be row finite and the cycles in E form an artinian partial ordered set
under a defined preorder. When the graph E is finite, the above graphical
conditions were shown to be equivalent to the algebra L having finite
Gelfand-Kirillov dimension in a paper by Alahmadi, Alsulami, Jain and Zelmanov.
Examples are constructed showing that this equivalence no longer holds if the
graph is infinite and a complete description is obtained of Leavitt path
algebras over arbitrary graphs having finite Gelfand-Kirillov dimension
