We can compare Corollary 3.1 with the results of , where the authors conducted a computational analysis of R -1/2 (G) in the dense Erdős-Rényi model. Specifically, they plotted the average Randić index against the probability p for various orders of n and noted a transition from zero to n/2, with the rate of change increasing proportionally to n. This observation aligns well with the previous finding in the dense scenario. Additionally, when they re-plotted the curves as a function of np, they noticed that curves representing different graph sizes n overlapped, forming a single universal curve. This observation, and even the asymptotic behaviour of the curve, can be further understood by considering our sparse results, which indicate that when the product np = λ is constant, the classic Randić index over n/2 goes to a fixed value, and that it goes to 1 when λ goes to infinity.