More on “Connected (n, m)-graphs with minimum and maximum zeroth-order general Randić index”

Let GG be a graph and d(u)d(u) denote the degree of a vertex uu in GG. The zeroth-order general Randić index 0Rα(G)0Rα(G) of the graph GG is defined as ∑u∈V(G)d(u)α∑u∈V(G)d(u)α, where the summation goes over all vertices of GG and αα is an arbitrary real number. In this paper we correct the proof of the main Theorem 3.5 of the paper by Hu et al. [Y. Hu, X. Li, Y. Shi, T. Xu, Connected (n,m)(n,m)-graphs with minimum and maximum zeroth-order general Randić index, Discrete Appl. Math. 155 (8) (2007) 1044–1054] and give a more general Theorem. We finally characterize 1 for α<0α<0 the connected G(n,m)G(n,m)-graphs with maximum value 0Rα(G(n,m))0Rα(G(n,m)), where G(n,m)G(n,m) is a simple connected graph with nn vertices and mm edges.