Graph automorphisms with maximal projection distances

This paper introduces diametrical graph automorphisms. A graph automorphism is called diametrical if it has the property that the distance between each vertex and its image is equal to the diameter of the graph. The structure of diametrically automorphic graphs is examined. The complexity of recognizing these graphs is shown to be NP-complete in general, while efficient algorithms for cographs and circular arc graphs are developed. The notion of distance lower bounded automorphism is introduced in order to apply the results on diametrical automorphisms to a wider range of automorphisms.