Abstract
We study the potential and limitations of the voltage graph construction for producing small regular graphs of large girth. We determine the relation between the girth of the base graph and the lift, and we show that any base graph can be lifted to a graph of arbitrarily large girth. We determine upper bounds on the girths of voltage graphs with respect to the nilpotency class in the case of nilpotent groups or the length of the derived series in the case of solvable voltage groups. These results suggest the use of perfect groups, which we use to construct the smallest known cubic graphs of girths 29 and 30. We also construct the smallest known (5, 10)-graphs and (7, 8)-graphs.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
