Reference List: Graph Products of Groups and Monoids

I made this list because I needed to generalize this concept a bit in my paper Noncommutative Network Models.

Graph products of groups were introduced by Elisabeth Green in 1990 in her thesis. The idea was generalized to monoids by António Veloso da Costa in 2001.

It’s not a product of graphs, its a “product” of groups/monoids (by which I just mean a way of combining the groups/monoids) with partial commutativity relations expressed by a simple graph. A common line of research about graph products is whether a graph product of groups/monoids which have some property also has that property.

Here is some literature and some links that I found:

1. 1986 Chiswell, Right-angled Coxeter groups
2. 1987 Droms, Graph groups
3. 1987 Droms, Isomorphisms of graph groups
4. 1987 Droms, Subgroups of graph groups
5. 1989 Servatius, Automorphisms of graph groups
6. 1990 Green, Graph products of groups
7. 1991 Droms Lewin Servatius, Tree groups and the 4-string pure braid group
8. 1991 Baik Howie Pride, The identity problem for graph products of groups
9. 1992 Chiswell, The Euler characteristic of a graph product
10. 1992 Chiswell, The growth series of a graph product
11. 1993 VanWyk, Graph groups are biautomatic
12. 1995 Hermiller Meier, Algorithms and geometry for graph products of groups
13. 2000 Brown Bullejos Porter, Free crossed resolutions for graph products of groups
14. 2001 Veloso da Costa, Graph products of monoids
15. 2001 Veloso da Costa, On graph products of automatic monoids
16. 2002 Crisp Laca, On the Toeplitz algebras of right angled and finite type Artin groups
17. 2003 Barkauskas, Centralizers in graph products of groups
18. 2003 Radcliffe, Rigidity of graph products of groups
19. 2006 Fohry Kuske, On graph products of automatic and biautomatic monoids
20. 2006 Lohrey Senizergues, When is a graph product of groups virtually-free?
21. 2008 Fountain Kambites, Graph products of right cancellative monoids
22. 2012 Kim, Surface subgroups of graph products of groups
23. 2016 Karpuz Ates Cangul Cevik, Finite derivation type for graph products of monoids