Circular chromatic number of Cartesian product of signed graphs

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) (H,τ) is χc(G H,στ)=max\χc(G,σ),χc(H,τ)\ and the circular chromatic number of Cartesian product Type 2 (G,σ)' (H,τ) satisfies χc(G ' H,σ' τ)≤ 2max\χc(G),χc(H)\.