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, ) (H, ) is ₂ (G H, ) =\₂ (G, ), ₂ (H, ) \ and the circular chromatic number of Cartesian product Type 2 (G, ) ' (H, ) satisfies ₂ (G ' H, ') 2\₂ (G), ₂ (H) \.