Geodesic
The isomorphism problem for generalized Baumslag--Solitar groups with one mobile edge
Algebra i logika, Tome 56 (2017) no. 3, pp. 300-316.

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A generalized Baumslag–Solitar group ($GBS$ group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. Every $GBS$ group is the fundamental group $\pi_1(\mathbb A)$ of some graph labeled $\mathbb A$. This paper deals with the isomorphism problem for $GBS$ groups, which is the problem of determining whether $\pi_1(\mathbb A)\cong\pi_1(\mathbb B)$ for two given graphs labeled $\mathbb A$ and $\mathbb B$. We describe an algorithm that decides this problem for the case where one of the labeled graphs has one mobile edge.
Keywords: isomorphism problem, generalized Baumslag–Solitar group, labeled graph. 
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     author = {F. A. Dudkin},
     title = {The isomorphism problem for generalized {Baumslag--Solitar} groups with one mobile edge},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2017_56_3_a1/}
}
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F. A. Dudkin. The isomorphism problem for generalized Baumslag--Solitar groups with one mobile edge. Algebra i logika, Tome 56 (2017) no. 3, pp. 300-316. http://geodesic.mathdoc.fr/item/AL_2017_56_3_a1/

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