Journal of Graph Theory
Lattice grids and prisms are antimagic
Theoretical Computer Science
The antimagicness of the Cartesian product of graphs
Theoretical Computer Science
Antimagic labeling and canonical decomposition of graphs
Information Processing Letters
On a relationship between completely separating systems and antimagic labeling of regular graphs
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Antimagic labelling of vertex weighted graphs
Journal of Graph Theory
Factorization of products of hypergraphs: Structure and algorithms
Theoretical Computer Science
On antimagic labeling of regular graphs with particular factors
Journal of Discrete Algorithms
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An anti-magic labeling of a finite simple undirected graph with p vertices and q edges is a bijection from the set of edges to the integers {1,..., q} such that all p vertex sums are pairwise distinct, where the vertex sum on a vertex is the sum of labels of all edges incident to such vertex. A graph is called anti-magic if it has an anti-magic labeling. Hartsfield and Ringel [3] conjectured that all connected graphs except K2 are anti-magic. Recently, N. Alon et al [1] showed that this conjecture is true for p-vertex graphs with minimum degree Ω(log p). They also proved that complete partite graphs except K2 and graphs with maximum degree at least p–2 are anti-magic. In this article, some new classes of anti-magic graphs are constructed through Cartesian products. Among others, the toroidal grids Cm × Cn(the Cartesian product of two cycles), and the higher dimensional toroidal grids $C_{m_1} \times C_{m_2} \times ...... \times C_{m_t}$, are shown to be anti-magic. Moreover, the more general result is also proved to be true: H × Cn (hence Cn × H) is anti-magic, where H is an anti-magic k-regular graph, where k1.