3 research outputs found
Resolution of a conjecture about linking ring structures
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