Symmetric Set Coloring of Signed Graphs

Abstract There are many concepts of signed graph coloring which defined by assigning colors to the vertices graphs. These usually differ in number self-inverse used. We introduce a unifying concept for this kind elements from symmetric sets In first part paper, we study colorings with where is fixed. prove Brooks’-type theorem and upper bounds corresponding chromatic numbers terms underlying graph. results used second symset-chromatic $$\chi _\mathrm{sym}(G,\sigma )$$ χ sym ( G , σ ) $$(G,\sigma . show that gives minimum partition into independent non-bipartite antibalanced subgraphs. particular, ) \le \chi (G)$$ ≤ final section these can also be formalized as DP -colorings.