From that perspective, the implications of the observed long-run behavior of the classical Randić index of the Erdős-Rényi sparse random graph suggest the conjecture that E(G)/n → g(λ) when n → ∞. By the way, something similar was conjectured for the trees generated by the Barabasi-Albert model with parameter α in ; perhaps, the approach developed in this paper can be explored in the Barabasi-Albert model and coupled with equation (3.1) to say something about the asymptotic behavior of the energy. As an additional point, for the dense case, it is well known that almost all ER graphs over n vertices have energy of order n 3/2 ( 8 3π p(1 -p) + o(1)) . Actually, since the adjacency matrix of a random graph is a random matrix, the proof relies on one of the most important achievements in this field which is Wigner's semicircular law. In general, examining the classical Randić index of the Erdős-Rényi random graph can provide insight into the asymptotic trends of energy, such as hyperenergetic and hypoenergetic characteristics, and conversely .