Summary: Given a graph \(G=(V,E)\) and a finite set \(T\) of positive integers containing \(0,\) a \(T\)-coloring of \(G\) is a function \(f:V(G)\to Z^+\cup\{0\}\) for all \(u\neq w\) in \(V(G)\) such that if \(uw\in E(G)\) then \(|f(u)-f(w)|\notin T\). For a \(T\)-coloring \(f\) of \(G\), the \(f\)-span \(\mathrm{sp}_T^f(G)\) is the maximum value of \(|f(u)-f(w)|\) over all pairs \(u,w\) of vertices of \(G\). The \(T\)-span \(\mathrm{sp}_T(G)\) is the minimum \(f\)-span overall \(T\)-colorings of \(G\). The \(f\)-edge span of a \(T\)-coloring \(\mathrm{esp}_T^f(G)\) is the maximum value of \(|f(u)-f(w)|\) over all edges \(uw\) of \(G\). The \(T\)-edge span \(\mathrm{esp}_T(G)\) is the minimum \(f\)-edge span overall \(T\)-colorings of \(G\). This paper discusses the \(T\)-span and \(T\)-edge span of Cartesian, Join, Union and Tensor products of graphs. Also, we discuss the relation between Restricted span and Restricted edge span of graphs.