On Antimagic Labeling of Odd Regular Graphs

Construction of Antimagic Labeling for the Cartesian Product of Regular Graphs

Mathematics in Computer Science ◽

10.1007/s11786-011-0084-3 ◽

2011 ◽

Vol 5 (1) ◽

pp. 81-87 ◽

Cited By ~ 2

Author(s):

Oudone Phanalasy ◽

Mirka Miller ◽

Costas S. Iliopoulos ◽

Solon P. Pissis ◽

Elaheh Vaezpour

Keyword(s):

Cartesian Product ◽

Regular Graphs ◽

Antimagic Labeling

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Antimagic Labeling of Regular Graphs

Journal of Graph Theory ◽

10.1002/jgt.21905 ◽

2015 ◽

Vol 82 (4) ◽

pp. 339-349 ◽

Cited By ~ 16

Author(s):

Feihuang Chang ◽

Yu-Chang Liang ◽

Zhishi Pan ◽

Xuding Zhu

Keyword(s):

Regular Graphs ◽

Antimagic Labeling

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Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers

Journal of Mathematics ◽

10.1155/2021/4627151 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Yi-Wu Chang ◽

Shan-Pang Liu

Keyword(s):

Complete Graphs ◽

Regular Graphs ◽

Real Numbers ◽

Cartesian Products ◽

Antimagic Labeling ◽

Edge Labeling

An edge labeling of graph G with labels in A is an injection from E G to A , where E G is the edge set of G , and A is a subset of ℝ . A graph G is called ℝ -antimagic if for each subset A of ℝ with A = E G , there is an edge labeling with labels in A such that the sums of the labels assigned to edges incident to distinct vertices are different. The main result of this paper is that the Cartesian products of complete graphs (except K 1 ) and cycles are ℝ -antimagic.

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On a Relationship between Completely Separating Systems and Antimagic Labeling of Regular Graphs

Lecture Notes in Computer Science - Combinatorial Algorithms ◽

10.1007/978-3-642-19222-7_24 ◽

2011 ◽

pp. 238-241 ◽

Cited By ~ 3

Author(s):

Oudone Phanalasy ◽

Mirka Miller ◽

Leanne Rylands ◽

Paulette Lieby

Keyword(s):

Regular Graphs ◽

Antimagic Labeling

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On antimagic labeling of regular graphs with particular factors

Journal of Discrete Algorithms ◽

10.1016/j.jda.2013.06.008 ◽

2013 ◽

Vol 23 ◽

pp. 76-82 ◽

Cited By ~ 2

Author(s):

Tao-Ming Wang ◽

Guang-Hui Zhang

Keyword(s):

Regular Graphs ◽

Antimagic Labeling

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Another Antimagic Conjecture

Symmetry ◽

10.3390/sym13112071 ◽

2021 ◽

Vol 13 (11) ◽

pp. 2071

Author(s):

Rinovia Simanjuntak ◽

Tamaro Nadeak ◽

Fuad Yasin ◽

Kristiana Wijaya ◽

Nurdin Hinding ◽

...

Keyword(s):

Connected Graph ◽

Disjoint Union ◽

Regular Graphs ◽

Computational Results ◽

Antimagic Labeling

An antimagic labeling of a graph G is a bijection f:E(G)→{1,…,|E(G)|} such that the weights w(x)=∑y∼xf(y) distinguish all vertices. A well-known conjecture of Hartsfield and Ringel (1990) is that every connected graph other than K2 admits an antimagic labeling. For a set of distances D, a D-antimagic labeling of a graph G is a bijection f:V(G)→{1,…,|V(G)|} such that the weightω(x)=∑y∈ND(x)f(y) is distinct for each vertex x, where ND(x)={y∈V(G)|d(x,y)∈D} is the D-neigbourhood set of a vertex x. If ND(x)=r, for every vertex x in G, a graph G is said to be (D,r)-regular. In this paper, we conjecture that a graph admits a D-antimagic labeling if and only if it does not contain two vertices having the same D-neighborhood set. We also provide evidence that the conjecture is true. We present computational results that, for D={1}, all graphs of order up to 8 concur with the conjecture. We prove that the set of (D,r)-regular D-antimagic graphs is closed under union. We provide examples of disjoint union of symmetric (D,r)-regular that are D-antimagic and examples of disjoint union of non-symmetric non-(D,r)-regular graphs that are D-antimagic. Furthermore, lastly, we show that it is possible to obtain a D-antimagic graph from a previously known distance antimagic graph.

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