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

Hubard, Isabel (author), Potočnik, Primož (author), Šparl, Primož (author)

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 surface, as well as a skeleton of a reflexible map on a non-orientable surface. This family consists of all lexicographic products $C_n[mK_1]$, where $m \ge 3, n=sm$, with $s$ an integer not divisible by $4$. This answers a question posed by Wilson in 2002.

• Language: English
• Keywords: rotary maps, chiral maps, orientable reflexible maps, non-orientable rotary maps
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics; PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2026
• Year: 2026
• Number of pages: Str. 384-403
• Numbering: Vol. 176
• PID: 20.500.12556/RUL-175133
• UDC: 519.17
• ISSN on article: 0095-8956
• DOI: 10.1016/j.jctb.2025.10.001
• COBISS.SI-ID: 253641731
• Publication date in RUL: 17.10.2025

Record is a part of a journal

• Title: Journal of combinatorial theory
• Shortened title: J. comb. theory, Ser. B
• Publisher: Elsevier
• ISSN: 0095-8956
• COBISS.SI-ID: 25721600

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.