On the Iteration of Graph Labelings

Abstract

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 $|f(u)–f(v)|$. In this paper we investigate the iteration of such graph labelings.