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arXiv · 2305.04261

Resolution of a conjecture about linking ring structures

Marston Conder·Luke Morgan·Primož Potočnik
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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, 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.

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Marston Conder, Luke Morgan, Primož Potočnik. 2023-05-23. Resolution of a conjecture about linking ring structures. https://arxiv.org/abs/2305.04261

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