Two-dimensional quantum gravity - A laboratory for fluctuating graphs and quenched connectivity disorder

This paper gives a brief introduction to using two-dimensional discrete and Euclidean quantum gravity approaches as a laboratory for studying the properties of fluctuating and frozen random graphs in interaction with "matter fields" represented by simple spin or vertex models. Due to the existence of numerous exact analytical results and predictions for comparison with simulational work, this is an interesting and useful enterprise. © W.Janke, D.A.Johnston, M.Weigel.