The null set of the join of paths
For positive integer k, a graph G is said to be k-magic if the edges of G can be labeled with the nonzero elements of Abelian group ℤ k, where ℤ 1= ℤ (the set of integers) and ℤ k is the group of integers mod k≥ 2, so that the sum of the labels of the edges incident to any vertex of G is the same. W...
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| Main Authors: | , |
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| Format: | text |
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Archīum Ateneo
2019
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| Online Access: | https://archium.ateneo.edu/mathematics-faculty-pubs/122 https://www.worldscientific.com/doi/abs/10.1142/S1793557119500608 |
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| Institution: | Ateneo De Manila University |
| Summary: | For positive integer k, a graph G is said to be k-magic if the edges of G can be labeled with the nonzero elements of Abelian group ℤ k, where ℤ 1= ℤ (the set of integers) and ℤ k is the group of integers mod k≥ 2, so that the sum of the labels of the edges incident to any vertex of G is the same. When this constant sum is 0, we say that G is a zero-sum k-magic graph. The set of all k for which G is a zero-sum k-magic graph is the null set of G. In this paper, we will completely determine the null set of the join of a finite number of paths. |
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