Extremality of degree-based graph entropies

Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. Based on Shannon’s entropy, we study graph entropies which are based on vertex degrees by using so-called information functionals. When considering Shannon entropy-based graph measures, there has been very little work to find their extremal values. The main contribution of this paper is to prove some extremal values for the underlying graph entropy of certain families of graphs and to find the connection between the graph entropy and the sum of degree powers. Further, conjectures to determine extremal values of graph entropies are given.