New Families of tripartite graphs with local antimagic chromatic number 3
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909286134710272 |
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| author | Lau, Gee-Choon Shiu, Wai Chee |
| author_facet | Lau, Gee-Choon Shiu, Wai Chee |
| contents | For a graph $G(V,E)$ of size $q$, a bijection $f : E(G) \to [1,q]$ is a local antimagc labeling if it induces a vertex labeling $f^+ : V(G) \to \mathbb{N}$ such that $f^+(u) \ne f^+(v)$, where $f^+(u)$ is the sum of all the incident edge label(s) of $u$, for every edge $uv \in E(G)$. In this paper, we make use of matrices of fixed sizes to construct several families of infinitely many tripartite graphs with local antimagic chromatic number 3. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_06703 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New Families of tripartite graphs with local antimagic chromatic number 3 Lau, Gee-Choon Shiu, Wai Chee Combinatorics 05C78, 05C69 For a graph $G(V,E)$ of size $q$, a bijection $f : E(G) \to [1,q]$ is a local antimagc labeling if it induces a vertex labeling $f^+ : V(G) \to \mathbb{N}$ such that $f^+(u) \ne f^+(v)$, where $f^+(u)$ is the sum of all the incident edge label(s) of $u$, for every edge $uv \in E(G)$. In this paper, we make use of matrices of fixed sizes to construct several families of infinitely many tripartite graphs with local antimagic chromatic number 3. |
| title | New Families of tripartite graphs with local antimagic chromatic number 3 |
| topic | Combinatorics 05C78, 05C69 |
| url | https://arxiv.org/abs/2408.06703 |