### Abstract

The connective constantμ(G) of a graph G is the asymptotic growth rate of the number σ_{n} of self-avoiding walks of length n in 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} for some constant A_{G} that depends on G. In the case of products of finite graphs μ(G) can be calculated explicitly and is shown to be an algebraic number.

Original language | English |
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Pages (from-to) | 325-332 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 340 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Mar 2017 |

### Keywords

- Connective constant
- Free product of graphs
- Self-avoiding walk

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Gilch, L. A., & Müller, S. (2017). Counting self-avoiding walks on free products of graphs.

*Discrete Mathematics*,*340*(3), 325-332. https://doi.org/10.1016/j.disc.2016.08.018