A conjecture on strong magic labelings of 2-regular graphs

Autor:	Jeremy Holden, Dan McQuillan, James M. McQuillan
Rok vydání:	2009
Předmět:	Vertex (graph theory) Discrete mathematics Conjecture Edge-graceful labeling Magic (programming) Strong vertex-magic Strong edge-magic Super vertex-magic Theoretical Computer Science 2-regular Combinatorics Labeling Discrete Mathematics and Combinatorics Regular graph Graph labelling Mathematics
Zdroj:	Discrete Mathematics. 309:4130-4136
ISSN:	0012-365X
Popis:	Let sC"3 denote the disjoint union of s copies of C"3. For each integer t>=2 it is shown that the disjoint union C"5@?(2t)C"3 has a strong vertex-magic total labeling (and therefore it must also have a strong edge-magic total labeling). For each integer t>=3 it is shown that the disjoint union C"4@?(2t-1)C"3 has a strong vertex-magic total labeling. These results clarify a conjecture on the magic labeling of 2-regular graphs, which posited that no such labelings existed. It is also shown that for each integer t>=1 the disjoint union C"7@?(2t)C"3 has a strong vertex-magic total labeling. The construction employs a technique of shifting rows of (newly constructed) Kotzig arrays to label copies of C"3. The results add further weight to a conjecture of MacDougall regarding the existence of vertex-magic total labeling for regular graphs.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ecd8613cced531ee13cde8c3e8972bb7 https://doi.org/10.1016/j.disc.2008.12.020 Zobrazit plný text záznamu Full Text from ScienceDirect