Self-reverse labelings of distance magic graphs

Kovář, Petr (author), Rozman, Ksenija (author), Šparl, Primož (author)

A graph is distance magic if it admits a bijective labeling of its vertices by integers from 1 up to the order of the graph in such a way that the sum of the labels of all the neighbors of a vertex is independent of a given vertex. We introduce the concept of a self-reverse distance magic labeling of a regular graph which allows for a more compact description of the graph and the labeling in terms of the corresponding quotient graph. We show that the members of several known infinite families of tetravalent distance magic graphs admit such labelings. We present a novel general construction producing a new distance magic graph from two existing ones. Using it we show that for each integer n ≥ 6, except for the odd integers up to 19, there exists a connected tetravalent graph of order n admitting a self-reverse distance magic labeling. We also determine all connected tetravalent graphs up to order 30 admitting a self-reverse distance magic labeling. The obtained data suggests a number of natural interesting questions giving several possibilities for future research.

• Language: English
• Keywords: distance magic, regular, self-reverse, classification
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: 22 str.
• Numbering: Vol. 49, iss. 1, art. 48
• PID: 20.500.12556/RUL-180463
• UDC: 519.17
• ISSN on article: 2180-4206
• COBISS.SI-ID: 271073027
• Publication date in RUL: 10.03.2026

Record is a part of a journal

• Title: Bulletin of the Malaysian mathematical sciences society
• Publisher: Springer Nature
• ISSN: 2180-4206
• COBISS.SI-ID: 512695613

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.

Secondary language

• Language: Slovenian
• Keywords: magija na daljavo, samodejna obrnitev