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. Potočnik and S. Wilson (2014) [12], 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.
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