Resolution of a conjecture about linking ring structures
Combinatorics
2023-05-24 v2 Group Theory
Abstract
An LR-structure is a tetravalent vertex-transitive graph together with a special type of a decomposition of its edge-set into cycles. LR-structures were introduced in a paper by P. Poto\v{c}nik and S. Wilson, titled `Linking rings structures and tetravalent semisymmetric graphs', in Ars Math. Contemp. 7 (2014), as a tool to study tetravalent semisymmetric graphs of girth 4. In this paper, we use the methods of group amalgams to resolve some problems left open in the above-mentioned paper.
Cite
@article{arxiv.2305.04261,
title = {Resolution of a conjecture about linking ring structures},
author = {Marston Conder and Luke Morgan and Primož Potočnik},
journal= {arXiv preprint arXiv:2305.04261},
year = {2023}
}