On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion
All graph in this paper are simple, finite, and connected. Let be a labeling of a graph . The function is called antimagic rainbow edge labeling if for any two vertices and , all internal vertices in path have different weight, where the weight of vertex is the sum of its incident edges label. T...
| Published in: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Mathematics Department UIN Maulana Malik Ibrahim Malang
2021-11-01
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| Subjects: | |
| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/12796 |
| Summary: | All graph in this paper are simple, finite, and connected. Let be a labeling of a graph . The function is called antimagic rainbow edge labeling if for any two vertices and , all internal vertices in path have different weight, where the weight of vertex is the sum of its incident edges label. The vertex weight denoted by for every . If G has a antimagic rainbow edge labeling, then is a antimagic rainbow vertex connection, where the every vertex is assigned with the color . The antimagic rainbow vertex connection number of , denoted by , is the minimum colors taken over all rainbow vertex connection induced by antimagic rainbow edge labeling of . In this paper, we determined the exact value of the antimagic rainbow vertex connection number of path ( ), wheel ( ), friendship ( ), and fan ( ). |
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| ISSN: | 2086-0382 2477-3344 |