New for: D1, D2, D3, D4, D5
As example for these two directions I will review the Cayley-graph and define the Fundamental group of a graph. The Nielsen-Schreier Theorem shows that the fundamental group of a Graphs is free. Free groups continue to receive a lot of attention among group-theorists.
Warren Dicks showed in 1994 the equivalence of the strengthened Hanna
Neumann conjecture and the almalgamated graph conjecture. I will briefly describe the group theoretic side of this, and then in more detail explain the graph theoretic side.