Mathematics – Combinatorics
Scientific paper
2006-02-14
Mathematics
Combinatorics
10 pages, 2 figures
Scientific paper
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.
No associations
LandOfFree
Cartesian Products of Regular Graphs are Antimagic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Cartesian Products of Regular Graphs are Antimagic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cartesian Products of Regular Graphs are Antimagic will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-255197