On k-prime graphs
In the context of a simple undirected graph GG, a kk-prime labeling refers to assigning distinct integers from the set {k,k+1,…,∣V(G)∣+k−1}\left\{k,k+1,\ldots ,| V\left(G)| +k-1\right\} to its vertices, such that adjacent vertices in GG are labeled with numbers that are relatively prime to each othe...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2024-12-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2024-0097 |
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| Summary: | In the context of a simple undirected graph GG, a kk-prime labeling refers to assigning distinct integers from the set {k,k+1,…,∣V(G)∣+k−1}\left\{k,k+1,\ldots ,| V\left(G)| +k-1\right\} to its vertices, such that adjacent vertices in GG are labeled with numbers that are relatively prime to each other. If GG has a kk-prime labeling, we say that GG is a kk-prime graph (k-PG). In this article, we characterize when a graph up to order 6 is a k-PG and characterize when a graph of order 7 is a k-PG whenever kk and k+1k+1 are not divisible by 5. Also, we find a lower bound for the independence number of a k-PG. Finally, we study when a cycle is a k-PG. |
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| ISSN: | 2391-5455 |