An infinite family of simple graphs underlying chiral, orientable reflexible and non-orientable rotary maps
Year: 2025
Type: preprint
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].
Source: arXiv (Cornell University)
Authors: Hubard, Isabel, Poto\v{c}nik, Primo\v{z}, \v{S}parl, Primo\v{z}
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979305778
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