Some results on ends and automorphisms of graphs (Q1191917)

The investigations of \textit{R. Halin} [Math. Ann. 157, 125-137 (1964; Zbl 0125.117) and Abh. Math. Sem. Univ. Hamburg 39, 251-283 (1973; Zbl 0265.05118)], and the author and \textit{M. E. Watkins} [Eur. J. Comb. 5, 149-162 (1984; Zbl 0547.05040)] are continued. Nondirected connected infinite graphs \(X\) are studied, with particular attention to their ends. An automorphism \(\sigma\) of \(X\) is called a translation if \(0<| F|<\infty\) implies \(\sigma(F)\neq F\), where \(F\) is a subset of the vertex set of \(X\). Several results on ends, translations and strips are shown. It is known that the number of ends fixed by a translation equals either one or two. Among the results, two theorems deal with the existence of a translation fixing two ends.