Coloring a Dominating Set Without Conflicts: q-Subset Square Coloring

The Square Coloring of a graph G refers to coloring vertices such that any two distinct which are at distance most receive different colors. In this paper, we initiate the study related problem called subset square graphs. Broadly, studies dominating set using q Here aim is optimize number colors used. This also generalizes well-studied Efficient Dominating Set problem. We show $$q$$ -Subset NP-hard for all values even on bipartite further parameterized complexity when by structural parameters. bounds needed color some classes.