Further results on the radio number for some construction of the path, complete, and complete bipartite graphs

Let G be a connected graph with $diam\left(G\right)$ . Then $d(u,v)$ indicates the distance of u and v in G. For any pair of distinct vertices $u,v$ of G, mapping from $c:V\left(G\right)\to N$ such that $d_G(u,v)+\left|c\right(u)-c(v\left)\right|\ge diam\left(G\right)+1$ . The maximum label assigned to any vertex of G under a radio labeling c is known as the span of c. The radio number $rn\left(G\right)$ of G is defined as the minimum span among all possible radio labelings of G. This paper aims to determine the radio number $rn\left(c\right)$ for specific constructed families of graphs with diameter 3, such as $P_2^2\left(N_{(m,n)}\right)$ , $K_{3,m}\left(K_n^c\right)$ , $K_{3,m}\left(n{P}_3\right)$ , $K_{3,3}\left(2K_{1,n}\right)$ , and $K_5\left(F_3^n\right)$ .