Mobility of vertex-transitive graphs Original Research Article

We define the mobility of a graph automorphism as the minimum distance between a vertex of the graph and its image under the automorphism, and the absolute mobility of a graph as the maximum of the mobilities of its automorphisms. In this paper, we investigate the mobility of certain classes of graphs, in particular, Cartesian and lexicographic products, vertex-transitive graphs, and Cayley graphs.