Sharp bounds of the zeroth-order general Randi? index of bicyclic graphs with given pendent vertices

摘要

Let G be a simple connected graph and α be a given real number. The zeroth-order general Randi? index of ~0R_α (G) is defined as ∑ν∈V(G)[d_G(ν)]~α, where d_G(ν) denotes the degree of the vertex ν of G. In this paper, for any α(≠0,1), we give sharp bounds of the zeroth-order general Randi?index ~0R_αof all bicyclic graphs with n vertices and k pendent vertices.