This paper investigates the radio labeling of friendship networks (F3,k, F4,k, F5,k, and F6,k). In contrast, a mathematical model is proposed for determining the upper bound of radio numbers for (F3,k, F4,k, F5,k, and F6,k). A computational investigation is presented to demonstrate that our results are superior to those of the past. In conclusion, the empirical study demonstrates that the proposed results surpass the previous ones in terms of the upper bound of the radio number and the run-time.
