The Chromatic Entropy of Linear Supertrees and Its Application

Abstract

Shannon entropy plays an important role in the field of information theory, and various graph entropies, including the chromatic entropy, have been proposed by researchers based on Shannon entropy with different graph variables. The applications of the graph entropies are found in numerous areas such as physical chemistry, medicine, and biology. The present research aims to study the chromatic entropy based on the vertex strong coloring of a linear p-uniform supertree. The maximal and minimal values of the p-uniform supertree are determined. Moreover, in order to investigate the generalization of dendrimers, a new class of p-uniform supertrees called hyper-dendrimers is proposed. In particular, the extremal values of chromatic entropy found in the research for supertrees are applied to explore the behavior of the hyper-dendrimers.

Keywords

• chromatic entropy
• vertex coloring
• linear uniform supertree
• dendrimer