Lattice grids and prisms are antimagic

Cheng, Yongxi

doi:10.1016/j.tcs.2006.12.003

Cited by 25 publications

(17 citation statements)

References 3 publications

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“…In 2009, D. Cranston [7] proved that all regular bipartite graphs are antimagic. While many various types of graphs have been shown to be antimagic [2,3,4,5,6,10,11,17,18], the question of antimagic-ness of regular graphs still remains open. In this paper, we consider the antimagic labeling of certain classes of regular graphs with perfect matchings.…”

Section: Definition 1 For a Graph G = (V E) With Q Edges And Withoumentioning

confidence: 99%

On Antimagic Labeling of Odd Regular Graphs

Wang

Zhang

2012

Lecture Notes in Computer Science

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Abstract. An antimagic labeling of a finite simple undirected graph with q edges is a bijection from the set of edges to the set of integers {1, 2, · · · , q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling. It was conjectured by N. Hartsfield and G. Ringel in 1990 that all connected graphs besides K2 are antimagic. Another weaker version of the conjecture is every regular graph is antimagic except K2. Both conjectures remain unsettled so far. In this article, certain classes of regular graphs of odd degree with particular type of perfect matchings are shown to be antimagic. As a byproduct, all generalized Petersen graphs and some subclass of Cayley graphs of Zn are antimagic.

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Section: Definition 1 For a Graph G = (V E) With Q Edges And Withoumentioning

confidence: 99%

On Antimagic Labeling of Odd Regular Graphs

Wang

Zhang

2012

Lecture Notes in Computer Science

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“…Hefetz [14] used the combinatorial nullstellensatz to prove that a graph with 3 k vertices, where k is a positive integer, and admits a K 3 -factor, is antimagic. Various papers on the antimagicness of particular classes of graphs have been published, for example, see [9,18,19,21,22]. For more details on antimagic labeling for particular classes of graphs see the dynamic survey [12], see also [5].…”

Section: Introductionmentioning

confidence: 99%

Approximate results for rainbow labelings

Lladó

Miller

2016

Period Math Hung

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Abstract. A simple graph G = (V, E) is said to be antimagic if there exists a bijection f : E → [1, |E|] such that the addition of the values of f on edges incident to every vertex are pairwise different. The graph G = (V, E) is distance antimagic if there exists a bijection f : V → [1, |V |], such that ∀x, y ∈ V,Using the polynomial method of Alon we prove that there are antimagic injections of any graph G with n vertices and m edges in the interval [1, 2n + m − 5] and, for trees with k base inner vertices, in the interval [1, m + k]. In particular, a tree all of whose nonleaves are adjacent to a leaf is antimagic. This gives a partial positive answer to a conjecture by Hartsfield and Ringel.We also show that there are distance antimagic injections of a graph G with order n and maximum degree ∆ in the interval [1, n + t(n − t)], where t = min{∆, n 2 }, and, for trees with k endvertices, in the interval [1, 3n − 4k]. In particular, all trees with n = 2k vertices and no pairs of incident leaves are distance antimagic, a partial solution to a conjecture of Arumugam.

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“…Kaplan et al proved that if a tree T has at most one vertex of degree 2, then T is antimagic (an error in the proof is corrected in ). The Cartesian products of various graphs are shown to be antimagic in .…”

Section: Introductionmentioning

confidence: 99%

Antimagic labelling of vertex weighted graphs

Wong

Zhu

2011

Journal of Graph Theory

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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, e∈E(v) f (e) = e∈E (u) f (e). 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, e∈E(v) f (e)+w(v) = e∈E(u) f (e)+w(u). A well-known conjecture asserts that every connected graph G = K 2 is 0-antimagic. On the other hand, there are connected graphs G = K 2 which are not weighted-1-antimagic. It is unknown whether every connected graph G = K 2 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.

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Lattice grids and prisms are antimagic

Cited by 25 publications

References 3 publications

On Antimagic Labeling of Odd Regular Graphs

On Antimagic Labeling of Odd Regular Graphs

Approximate results for rainbow labelings

Antimagic labelling of vertex weighted graphs

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