A conjecture on bipartite graphical regular representations
Abstract
In this paper we are concerned with the classification of the finite groups admitting a bipartite DRR and a bipartite GRR. First, we find a natural obstruction in a finite group for not admitting a bipartite GRR. Then we give a complete classification of the finite groups satisfying this natural obstruction and hence not admitting a bipartite GRR. Based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite GRR. Next, we prove the existence of bipartite DRRs for most of the finite groups not admitting a bipartite GRR found in this paper. Actually, we prove a much stronger result: we give an asymptotic enumeration of the bipartite DRRs over these groups. Again, based on these results and on some extensive computer computations, we state a conjecture aiming to give a complete classification of the finite groups admitting a bipartite DRR.
Cite
@article{arxiv.2001.03918,
title = {A conjecture on bipartite graphical regular representations},
author = {Jia-Li Du and Yan-Quan Feng and Pablo Spiga},
journal= {arXiv preprint arXiv:2001.03918},
year = {2020}
}
Comments
19 pages