I've been recently doing research on highly symmetric tilings of surfaces, which led to learning of an interesting theorem in graph theory (Weiss, 1974): Define a graph G be as a set V of nodes each pair of which either is or is not connected by an edge. We identify the pair of nodes with the edge. Let an n-arc on G be defined as a sequence of distinct nodes v_j, 0 <= j <= n, such that {v_(j-1),v_j} is an edge for 1 <= j <= n. Define a graph to be "n-arc symmetric" if, for any n-arcs A and B of G, there is a graph isomorphism G -> G taking A onto B. Theorem: If G is n-arc symmetric, then n <= 7. Anyone know anything about this theorem? The only write-up I could find is the original paper, in German, not a language I'm strong in: Weiss, R. M. "Über s-reguläre Graphen." J. Combin. Th. Ser. B 16, 229-233, 1974. (Something I read said this theorem depends on the classification of the sporadic simple groups. But since I think that was completed after 1974, perhaps the universality of this theorem became known only after the sporadic simple groups were known?) --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx