  By coloring a signed graph by signed colors, one obtains the signed chromatic
polynomial of the signed graph. For each signed graph we construct graded
cohomology groups whose graded Euler characteristic yields the signed chromatic
polynomial of the signed graph. We show that the cohomology groups satisfy a
long exact sequence which corresponds to signed deletion-contraction rule. This
work is motivated by Helme-Guizon and Rong's construction of the
categorification for the chromatic polynomial of unsigned graphs.
