Minimum Randic Index of Trees with Fixed Total Domination Number

The Randic index is among the most famous degree-based topological indices in chemical graph theory. It was introduced due to its application in modeling the properties of certain molecular structures and has been extensively studied. In this paper, we study the lower bound of the Randic index of trees in terms of the order and the total domination number. Finally, trees with the minimal Randic index are characterized.

Automated summary

This paper studies the lower bound of the Randic index of trees in terms of the order and the total domination number, and characterizes the trees with the minimal Randic index.