Cayley graphs, constructed from the algebraic structure of groups, provide a natural framework for exploring complex combinatorial properties. In these graphs, vertices represent group elements and ...

Cayley graphs provide a powerful and intuitive framework linking group theory with graph theory by representing groups through vertices and edges defined by a generating set. In the realm of finite ...

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We consider two stationary versions of the Eden model, on the upper half planar lattice, resulting in an infinite forest covering the half plane. Under weak assumptions on the weight distribution and ...

Motivated by the Benjamini-Schramm non-unicity of percolation conjecture we study the following question. For a given finitely generated non-amenable group Γ, does there exist a generating set S such ...

It is commonly believed that vertex-transitive graphs (and in particular Cayley graphs) tend to contain hamilton cycles. The only known connected vertex-transitive graphs without hamilton cycles are K ...