Zeroth-order general Randi´c index of trees

Abstract

Randi\'{c} indices belong to the most well-known topological indices. We study a very general index called the zeroth-order general Randi\'{c} index. We present upper and lower bounds on the zeroth-order general Randi\'{c} index for trees with given order and independence number, and for trees with given order and domination number. We also show that the bounds are best possible.

Minimum Randić Index of Trees with Fixed Total Domination Number

“…Moreover, the corresponding extremal graphs are characterized. In the paper, [13], upper and lower bounds on the zeroth-order general Randić index for trees with a given order and domination number are presented. In addition, the authors showed that the bounds are the best possible.…”