arXiv Open Access 2025

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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Abstrak

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].

Topik & Kata Kunci

math.CO

Penulis (3)

Isabel Hubard

Primož Potočnik

Primož Šparl

Format Sitasi

APA MLA BibTeX

Hubard, I., Potočnik, P., Šparl, P. (2025). An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps. https://arxiv.org/abs/2503.13243

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓