Cartesian Products of Regular Graphs are Antimagic
| dc.creator | Cheng, Yongxi | |
| dc.date | 2006-02-14 | |
| dc.date | 2006-04-21 | |
| dc.date.accessioned | 2026-07-07T07:03:26Z | |
| dc.date.available | 2026-07-07T07:03:26Z | |
| dc.description | An \emph{antimagic labeling} of a finite undirected simple graph with $m$ edges and $n$ vertices is a bijection from the set of edges to the integers $1,...,m$ such that all $n$ vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges incident with the same vertex. A graph is called \emph{antimagic} if it has an antimagic labeling. In 1990, Hartsfield and Ringel \cite{HaRi} conjectured that every simple connected graph, but $K_2$, is antimagic. In this article, we prove that a new class of Cartesian product graphs are antimagic. In addition, by combining this result and the antimagicness result on toroidal grids (Cartesian products of two cycles) in \cite{Wan}, all Cartesian products of two or more regular graphs can be proved to be antimagic. | |
| dc.description | 10 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0602319 | |
| dc.identifier | http://arxiv.org/abs/math/0602319 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108972 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C78 | |
| dc.title | Cartesian Products of Regular Graphs are Antimagic | |
| dc.type | text |