Extremality of Graph Entropy Based on Degrees of Uniform Hypergraphs with Few Edges

Let H be a hypergraph with n vertices. Suppose that d₁,d₂,…,d_n are degrees of the vertices of H. The t-th graph entropy based on degrees ofH is defined as Idt(H)=−∑i=1n(dit∑j=1ndjtlogdit∑j=1ndjt)=log(∑i=1ndit)−∑i=1n(dit∑j=1ndjtlogdit), where t is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of Idt(H) for t = 1, when H is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.