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arXiv · 2503.13243

An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps

Isabel Hubard·Primož Potočnik·Primož Šparl
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Abstract

In this paper, we provide the first known infinite family of simple graphs, each of which is the skeleton of a chiral map, a skeleton of a reflexible map on an orientable surfaces, as well as a skeleton of a reflexible map on a non-orientable surface. This family consists of all lexicographic product $C_n[mK_1]$, where $m\ge 3$, $n = sm$, with $s$ an integer not divisible by $4$. This answers a question posed in [S.\ Wilson, Families of regular graphs in regular maps, {\em Journal of Combinatorial Theory, Series B} 85 (2002), 269--289].

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Isabel Hubard, Primož Potočnik, Primož Šparl. 2025-03-17. An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps. https://arxiv.org/abs/2503.13243

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