Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers
An edge labeling of graph G with labels in A is an injection from EG to A, where EG 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=EG, there is an edge labeling with labels in A such that the sums of the labels assigned to edges inciden...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4627151 |
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| author | Yi-Wu Chang Shan-Pang Liu |
| author_facet | Yi-Wu Chang Shan-Pang Liu |
| author_sort | Yi-Wu Chang |
| collection | DOAJ |
| description | An edge labeling of graph G with labels in A is an injection from EG to A, where EG 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=EG, 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 K1) and cycles are ℝ-antimagic. |
| format | Article |
| id | doaj-art-9913a9f57972404cb9234ec398bb73a3 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9913a9f57972404cb9234ec398bb73a32025-02-03T01:04:12ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/4627151Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real NumbersYi-Wu Chang0Shan-Pang Liu1Department of Mathematical SciencesDepartment of Mathematical SciencesAn edge labeling of graph G with labels in A is an injection from EG to A, where EG 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=EG, 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 K1) and cycles are ℝ-antimagic.http://dx.doi.org/10.1155/2021/4627151 |
| spellingShingle | Yi-Wu Chang Shan-Pang Liu Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers Journal of Mathematics |
| title | Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers |
| title_full | Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers |
| title_fullStr | Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers |
| title_full_unstemmed | Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers |
| title_short | Cartesian Products of Some Regular Graphs Admitting Antimagic Labeling for Arbitrary Sets of Real Numbers |
| title_sort | cartesian products of some regular graphs admitting antimagic labeling for arbitrary sets of real numbers |
| url | http://dx.doi.org/10.1155/2021/4627151 |
| work_keys_str_mv | AT yiwuchang cartesianproductsofsomeregulargraphsadmittingantimagiclabelingforarbitrarysetsofrealnumbers AT shanpangliu cartesianproductsofsomeregulargraphsadmittingantimagiclabelingforarbitrarysetsofrealnumbers |