Sums of Powers of the Degrees of Graphs with k Cut Edges

For a graph G with k cut edges and a real number say α, we consider the sum, denoted by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R_{\alpha}^{0}(G)}$$\end{document}, of the αth powers of the degrees of the vertices of G. This sum is also called the zeroth-order general Randić index of the (molecular) graph G. We present some sharp bounds on this sum according to α in different intervals.