Metric properties of the Bethe lattice and the Husimi cactus

(Received 9 January 1992, accepted in final form 1 April 1992)

Abstract
The Bethe lattice and the Husimi cactus, traditionally viewed as graphs embedded in infinite-dimensional spaces, have been used to model a variety of problems. However, only their topological and connectivity properties are used in such models where the idea of metric distance between vertices and bond angles is meaningless. By following the indication of Mosseri and Sodac that such lattices can be embedded in two-dimensional hyperbolic spaces, we obtain metric properties for those structures and discuss further applications.