Let \(G\) be a simple connected graph with vertex set \(V\) and diameter \(d\). An injective function \(c: V\rightarrow \{1,2,3,\ldots\}\) is called a radio labeling of \(G\) if \({|c(x) c(y)|+d(x,y)\geq d+1}\) for all distinct \(x,y\in V\), where \(d(x,y)\) is the distance between vertices \(x\) and \(y\). The largest number in the range of \(c\) is called the span of the labeling \(c\). The radio number of \(G\) is the minimum span taken over all radio labelings of \(G\). For a fixed vertex \(z\) of \(G\), the sequence \((l_1,l_2,\ldots,l_r)\) is called the level tuple of \(G\), where \(l_i\) is the number of vertices whose distance from \(z\) is \(i\). Let\(J^k(l_1,l_2,\ldots,l_r)\) be the wedge sum (i.e. one vertex union) of \(k\geq2\) graphs having same level tuple \((l_1,l_2,\ldots,l_r)\). Let \(J(\frac{l_1}{l’_1},\frac{l_2}{l’_2},\ldots,\frac{l_r} {l’_r})\) be the wedge sum of two graphs of same order, having level tuples  \((l_1,l_2,\ldots,l_r)\) and \((l’_1,l’_2,\ldots,l’_r)\). In this paper, we compute the radio number for some sub-families of \(J^k(l_1,l_2,\ldots,l_r)\) and \(J(\frac{l_1}{l’_1},\frac{l_2}{l’_2},\ldots,\frac{l_r}{l’_r})\).

An antipodal labeling is a function \(f\ \)from the vertices of \(G\) to the set of natural numbers such that it satisfies the condition \(d(u,v) + \left| f(u) – f(v) \right| \geq d\), where d is the diameter of \(G\ \)and \(d(u,v)\) is the shortest distance between every pair of distinct vertices  \(u\) and \(v\) of \(G.\) The span of an antipodal labeling \(f\ \)is \(sp(f) = \max\{|f(u) – \ f\ (v)|:u,\ v\, \in \, V(G)\}.\) The antipodal number of~G, denoted by~an(G), is the minimum span of all antipodal labeling of~G. In this paper, we determine the antipodal number of Mongolian tent and Torus grid.