On the Iteration of Graph Labelings

A labeling (function) of a graph \(G\) is an assignment \(f\) of nonnegative integers to the vertices of \(G\). Such a labeling of \(G\) induces a labeling of \(L(G)\), the line graph of \(G\), by assigning to each edge \(uv\) of \(G\) the label \(\lvert f(u) – f(v)\rvert\). In this paper we investigate the iteration of such graph labelings.