AbstractIn this paper, we introduce and investigate a new graph invariant called the signed uniqueisolated perfect dom-chromatic number of a graph. This parameter unifies the notions of signeddomination, perfect domination, unique domination, isolated domination, and proper vertexcoloring. We establish fundamental bounds, structural properties, exact values for standard graphfamilies, and complexity results. The study positions the new parameter at the top of thedomination–coloring hierarchy and opens avenues for further research in domination theory andsigned graph invariants.
K.Muralidharan, S.Suganya, D. Vidhya, J. Satish Kumar (Wed,) studied this question.
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