On local antimagic chromatic numbers of the join of two special families of graphs
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911982737686528 |
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| author | Lau, Gee-Choon Shiu, Wai Chee |
| author_facet | Lau, Gee-Choon Shiu, Wai Chee |
| contents | It is known that null graphs and 1-regular graphs are the only regular graphs without local antimagic chromatic number. In this paper, we use matrices of size $(2m+1) \times (2k+1)$ to completely determine the local antimagic chromatic number of the join of null graphs, $O_m, m\ge 1,$ and 1-regular graphs of odd components, $(2k+1)P_2$, $k\ge 1$. Consequently, we obtained infinitely many (possibly disconnected or regular) tripartite graphs with local antimagic chromatic number 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On local antimagic chromatic numbers of the join of two special families of graphs Lau, Gee-Choon Shiu, Wai Chee Combinatorics 05C78, 05C69 It is known that null graphs and 1-regular graphs are the only regular graphs without local antimagic chromatic number. In this paper, we use matrices of size $(2m+1) \times (2k+1)$ to completely determine the local antimagic chromatic number of the join of null graphs, $O_m, m\ge 1,$ and 1-regular graphs of odd components, $(2k+1)P_2$, $k\ge 1$. Consequently, we obtained infinitely many (possibly disconnected or regular) tripartite graphs with local antimagic chromatic number 3. |
| title | On local antimagic chromatic numbers of the join of two special families of graphs |
| topic | Combinatorics 05C78, 05C69 |
| url | https://arxiv.org/abs/2408.04942 |