For any finite group A and any finitely generated group B, we prove that the corresponding
lamplighter group A≀ B admits a standard generating set with unbounded depth, and that if …

In 1982, Durnberger proved that every connected Cayley graph of a finite group with a
commutator subgroup of prime order contains a hamiltonian cycle. In this paper, we extend …

Asymptotic properties and Poisson boundaries of wreath products Page 1 Préparée à l’École
Normale Supérieure de Paris Asymptotic properties and Poisson boundaries of wreath …

For locally finite infinite graphs the notion of Hamilton cycles can be extended to Hamilton
circles, homeomorphic images of $ S^ 1$ in the Freudenthal compactification. In this paper …

We show that if $ C_1 $ and $ C_2 $ are directed cycles (of length at least two), then the
Cartesian product $ C_1\Box C_2 $ has two arc-disjoint hamiltonian paths.(This answers a …

Witte Morris showed in [21] that every connected Cayley graph of a finite (generalized)
dihedral group has a Hamiltonian path. The infinite dihedral group is defined as the free …

We show that Cayley graphs of groups which are either a free product with amalgamation
over a finite subgroup of index two or an HNNextension over a finite subgroup contain a …

In 1982, Durnberger proved that every connected Cayley graph of a finite group with a
commutator subgroup of prime order contains a hamiltonian cycle. In this paper, we extend …

NEIGHBOURHOOD-PRIME LABELING OF CERTAIN CLASSES OF CAYLEY GRAPHS
Page 1 Advances and Applications in Mathematical Sciences Volume 21, Issue 4, February …

This thesis deals with various topics concerning infinite graphs and finitely generated infinite
groups using many ideas from topological infinite graph theory and geometric group theory …