Hi, I am a PhD student from Theoretical Physics. Recently in my field of work I saw people using geometric group theory, Cayley graphs and Dehn functions to comment about certain properties of some models. I wanted to know, if there is a systematic way to generate Cayley graphs for free group along with relations for eg. If the generator set is {a,b} and for the free group with this generator set the Cayley graph is a 4 regular tree, If I impose the relation ab=ba the 4 regular tree becomes a 2D square lattice. I want to know that is there a systematic way to get the Cayley graphs for a given group like I described above and can I find properties of this graph like say the Dehn function and how the boundary nodes scale as depth with the Graph and etc. Is there a formal way to get the properties, I am sorry I am not very familar with rigorous Mathematical background, I have learned a bit about Geometric Group theory and also some basic graph theory. It would also be very helpful if you can recommend some material regarding this which is probably suited for a Theoretical Physicist. Thanks