The Chromatic Entropy of a p -Uniform Linear Unicyclic Hypergraph

Graph entropy is originated from Shannon entropy, which is used to quantify the complexity and uncertainty of networks and is widely applied in fields such as information theory, communication theory and statistics. As a kind of classical graph entropy, the chromatic entropy of a graph plays a key role in describing the structures of networks. Generally, a hypergraph is the extension of a graph, which is often used in characterising complex systems. In this paper, we investigate the chromatic entropy of linear p-uniform unicyclic hypergraphs based on strong vertex coloring. We determine the hypergraphs that attain the maximum and minimum chromatic entropy within this class. Using edge-moving operations, we characterize the extremal structures and derive explicit formulas for their entropy values.