On (4, 2)-Labeling of Certain Graphs

The \((4,2)\)-labeling of a graph \(G\) is a function \(f:V(G)→ {Z}^+\) such that \(|f(x)-f(y)|≥ 4\) if \(d(x,y)=1\) and \(|f(x)-f(y)|≥ 2\) if \(d(x,y)=2\), for any \(x,y∈ V(G)\). In this paper, we label different types of graphs such as paths, cycles, complete and complete bipartite graphs, star graphs and ladder graphs to study the bounds of the span \(λ\) of these graphs.