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 of$H$ is defined as $I_d^t\left(H\right)=-\sum i=1n(\frac{d_i^t}{{\sum }_{j=1}^n{d}_j^t}\log \frac{d_i^t}{{\sum }_{j=1}^n{d}_j^t})=\log (\sum i=1n{d}_i^t)-\sum i=1n(\frac{d_i^t}{{\sum }_{j=1}^n{d}_j^t}\log d_i^t),$ 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 $I_d^t\left(H\right)$ for t = 1, when $H$ is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.