RADIO NUMBER OF $P_{n}^{+++}$

Source abstract

Radio labeling is an important graph labeling technique that arises from frequency assignment problems in wireless communication networks, where interference between transmitters must be minimized. The radio number of a graph represents the minimum span required to assign labels to vertices while satisfying prescribed interference constraints based on vertex distances. In this paper, we investigate the radio number of the total transformation graph of the path graph $P_{n}^{+++}$. We study the structural properties of this transformed graph and establish lower and upper bounds for its radio number. Further, exact values are obtained for the even case, while tight bounds are derived for the odd case. The results presented in this work extend > existing research on radio labeling of transformed graphs and contribute to the study of graph labeling problems related to communication network optimization.