The  connective constant     μ(G)     μ   (  G  )         of a graph   G     G        is the asymptotic growth rate of the number   σ n        σ    n          of self-avoiding walks of length   n     n        in   G     G        from a given vertex. We prove a formula for the connective constant for free products of quasi-transitive graphs and show that   σ n ∼A G μ(G) n        σ    n    ∼    A    G    μ     (  G  )     n          for some constant   A G        A    G          that depends on   G     G       . In the case of products of finite graphs   μ(G)     μ   (  G  )         can be calculated explicitly and is shown to be an algebraic number.
['Lorenz A. Gilch', 'Sebastian Müller']
Counting self-avoiding walks on free products of graphs