{
  "id": "1509.03209",
  "version": "v1",
  "published": "2015-09-10T16:05:29.000Z",
  "updated": "2015-09-10T16:05:29.000Z",
  "title": "Counting self-avoiding walks on free products of graphs",
  "authors": [
    "Lorenz A. Gilch",
    "Sebastian Müller"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO",
    "math.GR",
    "math.PR"
  ],
  "abstract": "The connective constant $\\mu(G)$ of a graph $G$ is the asymptotic growth rate of the number $\\sigma_{n}$ 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 $\\sigma_{n}\\sim A_{G} \\mu(G)^{n}$ for some constant $A_{G}$ that depends on $G$. In the case of finite products $\\mu(G)$ can be calculated explicitly and is shown to be an algebraic number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-10T16:05:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "20E06",
      "60K35"
    ],
    "keywords": [
      "free products",
      "counting self-avoiding walks",
      "connective constant",
      "asymptotic growth rate",
      "finite products"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150903209G"
    }
  }
}