Abstract: A distance-transitive graph is a graph in which for every two ordered pairs ofvertices ▫$(u,v)$▫ and ▫$(u',v')$▫ such that the distance between ▫$u$▫ and ▫$v$▫ is equal to the distance between ▫$u'$▫ and ▫$v'$▫ there exists an automorphism of the graph mapping ▫$u$▫ to ▫$u'$▫ and ▫$v$▫ to ▫$v'$▫. A semiregular element of a permutation group is anon-identity element having all cycles of equal length in its cycle decomposition. It is shown that every distance-transitive graph admits a semiregular automorphism.Keywords: distance-transitive graph, vertex-transitive graph, semiregular automorphism, permutation groupPublished in RUP: 15.10.2013; Views: 3282; Downloads: 98 Link to full text
Keywords: cubic graph, symmetric, semiregular automorphism, tetracirculant, pentacirculantPublished in RUP: 15.10.2013; Views: 3056; Downloads: 95 Link to full text
Keywords: automorphism group, arc-transitive graph, semiregular automorphismPublished in RUP: 15.10.2013; Views: 3177; Downloads: 71 Link to full text
Keywords: graph, Cayley graph, arc-transitive, snark, semiregular automorphism, bicirculantPublished in RUP: 15.10.2013; Views: 3322; Downloads: 155 Link to full text