20.500.12556/RUL-180463 Self-reverse labelings of distance magic graphs 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. distance magic regular self-reverse classification magija na daljavo samodejna obrnitev true false true Angleški jezik Slovenski jezik Članek v reviji 2026-03-10 09:20:43 2026-03-10 09:20:44 2026-03-11 04:38:30 0000-00-00 00:00:00 2026 0 0 22 str. iss. 1, art. 48 Vol. 49 Feb. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17 2180-4206 271073027 RAZ_Kovař_Petr_2026.pdf RAZ_Kovař_Petr_2026.pdf 1 1E730FC5FCA241975D2BE955162C4D7E f04137c09e83ac210eb624bee8a7c20ebb58b2a5175e343d7e3464acbddb0dee 1e213b09-1c5b-11f1-a1ba-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=229885 https://link.springer.com/article/10.1007/s40840-026-02042-4 1 9cf080be-1c59-11f1-a1ba-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=229881 Pedagoška fakulteta 0 0 0