Circular chromatic number of Cartesian product of signed graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908760576884736 |
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| author | Desire, Ebode Atangana Pie |
| author_facet | Desire, Ebode Atangana Pie |
| contents | This paper studies the circular coloring of signed graphs. A signed graph is a graph with a signature that assigns a sign to each edge, either positive or negative. This paper studies circular coloring and a circular chromatic number of Type 1 and Type Cartesian products. We shall prove the following results: The circular chromatic number of Cartesian product Type 1 $(G,σ)\Box (H,τ)$ is $χ_{c}(G \Box H,σ\Boxτ)=\max\{χ_{c}(G,σ),χ_{c}(H,τ)\}$ and the circular chromatic number of Cartesian product Type 2 $(G,σ)\Box' (H,τ)$ satisfies $χ_{c}(G \Box' H,σ\Box' τ)\leq 2\max\{χ_{c}(G),χ_{c}(H)\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06360 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Circular chromatic number of Cartesian product of signed graphs Desire, Ebode Atangana Pie Combinatorics This paper studies the circular coloring of signed graphs. A signed graph is a graph with a signature that assigns a sign to each edge, either positive or negative. This paper studies circular coloring and a circular chromatic number of Type 1 and Type Cartesian products. We shall prove the following results: The circular chromatic number of Cartesian product Type 1 $(G,σ)\Box (H,τ)$ is $χ_{c}(G \Box H,σ\Boxτ)=\max\{χ_{c}(G,σ),χ_{c}(H,τ)\}$ and the circular chromatic number of Cartesian product Type 2 $(G,σ)\Box' (H,τ)$ satisfies $χ_{c}(G \Box' H,σ\Box' τ)\leq 2\max\{χ_{c}(G),χ_{c}(H)\}$. |
| title | Circular chromatic number of Cartesian product of signed graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.06360 |