Graph Coloring Based on Degree-Dominance Property

Graphs are widely used to model complex systems in social, biological, and technological domains.Motivated by the need to incorporate hierarchical influence within such networks, this study introduces domination coloring, a new coloring framework based on degree-domination.In a graph G = (V, E), each vertex v has degree d(v), and a vertex x is said to dominate an adjacent vertex y if d(x) > d(y).Under domination coloring, adjacent vertices must receive different colors whenever one dominates the other.This work establishes the theoretical foundations of domination coloring, proves essential structural properties, proposes efficient algorithms, and discusses potential applications in network analysis and decision-making environments.