Antipodal covers of strongly regular graphs

Aleksandar Jurišić
1998 Discrete Mathematics  
Antipodal covers of strongly regular graphs which are not necessarily distance-regular are studied. The structure of short cycles in an antipodal cover is considered. In most cases, this provides a tool to determine if a strongly regular graph has an antipodal cover. In these cases, covers cannot be distance-regular except when they cover a complete bipartite graph. A relationship between antipodal covers of a graph and its line graph is investigated. Finally, antipodal covers of complete
more » ... ite graphs and their line graphs are characterized in terms of weak resolvable transversal designs which are, in the case of maximal covering index, equivalent to affine planes with a parallel class deleted. This generalizes Drake's and Gardiner's characterization of distance-regular antipodal covers of complete bipartite graphs. Bipartite antipodal distance-regular graphs with odd diameter are characterized.
doi:10.1016/s0012-365x(97)00139-8 fatcat:shuni5ozqffhroi3psagupjgyy