Fractional coloring of product signed graphs

This study examines the fractional chromatic number associated with the direct product of signed graphs. It shows that if $(H,\tau)$ is a signed circulant graph $G(n,S,T)$, then for any signed graph $(G,\sigma)$, the fractional chromatic number of their direct product is the lower number between the fractional chromatic number of $(G,\sigma)$ and $(H,\tau)$.