Mutual embeddings of right-angled Artin groups and generalized Baumslag-Solitar groups

A finitely generated group $G$ acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag–Solitar group ($GBS$ group). In this paper, we study when a given $GBS$ group can be embedded in a right-angled Artin group ($RAAG$) and vice versa. An exhaustive description has been obtained in both cases. If an embedding exists, then we discuss its construction.