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arXiv · 2404.06360

Circular chromatic number of Cartesian product of signed graphs

Ebode Atangana Pie Desire
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Abstract

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 $χ_{c}(G \Box' H,σ\Box' τ)\leq 2\max\{χ_{c}(G),χ_{c}(H)\}$.

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Ebode Atangana Pie Desire. 2026-01-12. Circular chromatic number of Cartesian product of signed graphs. https://arxiv.org/abs/2404.06360

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