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,.,dn are degrees of the vertices of H. The t-th graph entropy based on degrees ofH is defined as Itd(H)=..i=1n(dti.nj=1dtjlogdti.nj=1dtj)=log(.i=1ndti)..i=1n(dti.nj=1dtjlogdti), 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 Itd(H) for t = 1, when H is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.