Some extremal graphs with respect to the zeroth-order general randic index

Abstract

For a given graph set it is important to find the upper and lower bounds for some graph invariant in and characterize the graphs in which the maximal and minimal values are attained, respectively. In this paper, we investigated several upper and lower bounds on the general zeroth-order Randic index of graphs in terms of number of cut edges, independence number and matching number, respectively. The extremal graphs are also completely characterized. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.