Symmetric set coloring of signed graphs

There are many approaches to signed graphs coloring. One of the main difference regards the number of self-inverse elements used. We develop a new coloring by using symmetric sets with different numbers of self-inverse elements. This approach provides a framework to describe all other ways of coloring signed graphs which are defined by assigning colors to the vertices of the graphs. We investigate the specific role of self-inverse colors in signed graph coloring and prove a Brooks’ type theorem for these colorings. We also show that this coloring can be formalized as a specific DP -coloring.