Novel Inequalities for Generalized Graph Entropies Revisited, Graph   Energies and Topological Indices
  The entropy of a graph is an information-theoretic quantity which expresses the complexity of a graph \cite{DM1,M}. After Shannon introduced the definition of entropy to information and communication, many generalizations of the entropy measure have been proposed, such as R\'enyi entropy and Dar\`oczy's entropy. In this article, we prove accurate connections (inequalities) between generalized graph entropies, distinct graph energies and topological indices. Additionally, we obtain some extremal properties of nine generalized graph entropies by employing distinct graph energies and topological indices. 
Xueliang Li, Zhongmei Qin, Meiqin Wei, Ivan Gutman, Matthias Dehmer
math.CO