I'm not familiarized with applied maths and perhaps this is a silly question. A silly answer is welcome if that is the case.
Trees in graph theory are cycleless graphs. Graph theory, most of it, is about finite graphs. Is there any theory about infinite trees that connects infinite graph theory and fractal theory? The point is to find a model for real trees (pines, olive trees, etc).
Graph theory is about essentially combinatorial objects - the mathematics you do when you know what is (abstractly) connected to what. Graphs may be infinite and they may be trees.
Fractals are geometrical objects, often created by some kind of branching process. You can construct an abstract tree that describes the branching, but what graph theory has to say about that tree won't tell you much about the fractal, nor will it tell you very much about branching in "real trees".