Self-reverse labelings of distance magic graphs

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

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.

• Jezik: Angleški jezik
• Ključne besede: distance magic, regular, self-reverse, classification
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2026
• Št. strani: 22 str.
• Številčenje: Vol. 49, iss. 1, art. 48
• PID: 20.500.12556/RUL-180463
• UDK: 519.17
• ISSN pri članku: 2180-4206
• COBISS.SI-ID: 271073027
• Datum objave v RUL: 10.03.2026

Gradivo je del revije

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

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: magija na daljavo, samodejna obrnitev