A self-avoiding walk (SAW) is a mathematical and combinatorial object used primarily in statistical mechanics and theoretical physics, as well as in computer science and graph theory. It is defined as a path that does not visit the same point more than once.
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An -step self-avoiding walk on a graph is a sequence of distinct graph vertices with an edge between successive graph vertices. It is a graph path with edges and graph vertices. On a transitive graph, the exponential growth rate of rooted self-avoiding walk counts is the connective constant.