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

Let Η be a hypergraph with n vertices. Suppose that di,￠/2,...,dn are degrees of the vert ices of Η. The t-th graph entropy based on degrees of H is defined as Id^t(Η)=-n∑i=1(di^t/∑j=1^ndj^t^nlogdi^t/∑j=1^ndj^t^n)=log(n∑i=1di^t)-n∑i=1(di^t/∑j=1^ndj^tlogdi^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 Id^t(Η) for t = 1, when Η is among all uniform super trees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.

Let ■ be a hypergraph with n vertices. Suppose that d1, d2,..., dn are degrees of the vertices of ■. The t-th graph entropy based on degrees of ■ is defined as ■,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 （■） for t = 1, when ■ is among all uniform supertrees, unicyclic uniform hypergraphs and bicyclic uniform hypergraphs, respectively.