20.500.12556/RUP-23023 Group distance magic cubic graphs A $\Gamma$-distance magic labeling of a graph $G = (V, E)$ with $|V| = n$ is a bijection $\ell$ from $V$ to an Abelian group $\Gamma$ of order $n$, for which there exists $\mu \in \Gamma$, such that the weight $w(x) =\sum_{y\in N(x)}\ell(y)$ of every vertex $x \in V$ is equal to $\mu$. In this case, the element $\mu$ is called the magic constant of $G$. A graph $G$ is called a group distance magic if there exists a $\Gamma$-distance magic labeling of $G$ for every Abelian group $\Gamma$ of order $n$. In this paper, we focused on cubic $\Gamma$-distance magic graphs as well as some properties of such graphs. $\Gamma$-razdaljno magično labeliranje grafa $G = (V, E)$ z $|V| = n$ je bijekcija $\ell$ iz $V$ v abelsko grupo $\Gamma$ reda $n$, za katerega obstaja $\mu \in \Gamma$, tako da je utež $w(x) =\sum_{y\in N(x)}\ell(y)$ vsakega vozlišča $x \in V$ enaka $\mu$. V tem primeru elementu $\mu$ magična konstanta grafa $G$. Graf $G$ je grupno razdaljno magičen, če obstaja $\Gamma$-razdaljno magično labeliranje grafa $G$ za vsako abelsko grupo $\Gamma$ reda $n$. V tem članku študiramo kubične grupno razdaljno magične grafe, kot tudi nekatere lastnosti teh grafov. group distance magic labeling Kotzig array generalized Petersen graph grupna razdaljno magična labeliranja Kotzigove razpredelnice posplošeni Petersenovi grafi true false true Angleški jezik Slovenski jezik Članek v reviji 2026-05-06 15:33:16 2026-05-06 15:33:18 2026-05-07 03:08:26 0000-00-00 00:00:00 2026 0 0 str. 465-481 no. 2 Vol. 46 2026 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2025-12-22 519.17 1234-3099 10.7151/dmgt.2613 277277443 RAZ_Cichacz_Sylwia_2026.pdf RAZ_Cichacz_Sylwia_2026.pdf 1 235681C4C421F0BD6A4570873F31A729 6865026eca6ed77ae3bcda962e5a2d03b922daee65477c9eba79dcfee74ae10c 3845853b-4950-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33642 https://www.dmgt.uz.zgora.pl/publish/article.php?doi=2613 1 11cb14e7-4950-11f1-9e8d-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=33641 Inštitut Andrej Marušič 0 0 0