Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number · arXivDesk2103.15288Mar 29, 2021
Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number
Chang Liu, Jianping Li
Abstract
The zeroth-order general Randić index of graph G=(VG,EG), denoted by 0Rα(G)
, is the sum of items
over all vertices
, where
is a pertinently chosen real number. In this paper, we obtain the sharp upper and lower bounds on
of trees with a domination number
, in intervals
α∈(−∞,0)∪(1,∞) and
, respectively. The corresponding extremal graphs of these bounds are also characterized.