Combinatorics, Probability and Computing
Lattice grids and prisms are antimagic
Theoretical Computer Science
Journal of Graph Theory
Anti-magic graphs via the Combinatorial NullStellenSatz
Journal of Graph Theory
An application of the combinatorial Nullstellensatz to a graph labelling problem
Journal of Graph Theory
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On antimagic labeling of regular graphs with particular factors
Journal of Discrete Algorithms
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Suppose G is a graph, k is a non-negative integer. We say G is k-antimagic if there is an injection f: E→{1, 2, …, |E| + k} such that for any two distinct vertices u and v, . We say G is weighted-k-antimagic if for any vertex weight function w: V→ℕ, there is an injection f: E→{1, 2, …, |E| + k} such that for any two distinct vertices u and v, . A well-known conjecture asserts that every connected graph G≠K2 is 0-antimagic. On the other hand, there are connected graphs G≠K2 which are not weighted-1-antimagic. It is unknown whether every connected graph G≠K2 is weighted-2-antimagic. In this paper, we prove that if G has a universal vertex, then G is weighted-2-antimagic. If G has a prime number of vertices and has a Hamiltonian path, then G is weighted-1-antimagic. We also prove that every connected graph G≠K2 on n vertices is weighted- ⌊3n/2⌋-antimagic. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc.