20.500.12556/RUP-21709 Tetravalent distance magic graphs of small order and an infinite family of examples Štirivalentni razdaljno magični grafi majhnega reda in neskončna družina primerov A graph of order ▫$n$▫ is distance magic if it admits a bijective labeling of its vertices with integers from ▫$1$▫ to ▫$n$▫ such that each vertex has the same sum of the labels of its neighbors. This paper contributes to the long term project of characterizing all tetravalent distance magic graphs. With the help of a computer we find that out of almost nine million connected tetravalent graphs up to order 16 only nine are distance magic. In fact, besides the six well known wreath graphs there are only three other examples, one of each of the orders 12, 14 and 16. We introduce a generalization of wreath graphs, the so-called quasi wreath graphs, and classify all distance magic graphs among them. This way we obtain infinitely many new tetravalent distance magic graphs. Moreover, the two non-wreath graphs of orders 12 and 14 are quasi wreath graphs while the one of order 16 can be obtained from a quasi wreath graph of order 14 using a simple construction due to Kovář, Fronček and Kovářová. distance magic tetravalent quasi wreath graph razdaljno magičen štirivalenten kvazi venčni graf true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Neznano 2025-09-10 13:51:47 2025-09-10 13:51:47 2025-10-24 23:21:03 0000-00-00 00:00:00 2025 0 0 13 str. no. 4, [article no.] P4.05 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-01-01 519.17 1855-3974 10.26493/1855-3974.3424.d5e 246243331 AMC_Rozman,Sparl_2025.pdf AMC_Rozman,Sparl_2025.pdf 1 5197FF147D317AE4F203537C005A90AF be37ecdfb79f873097e2aec7b66500f999913fffb51158246034f79d45a7a5d6 ab91a14f-8e3c-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31540 Založba Univerze na Primorskem 0 0 0