On the Constructions of New Families of Graceful Graphs

Abstract

Suppose that graphs \(H\) and \(G\) are graceful, and that at least one of \(H\) and \(G\) has an \(\alpha\)-labeling. Four graph operations on \(H\) and \(G\) are provided. By utilizing repeatedly or in turn the four graph operations, we can construct a large number of graceful graphs. In particular, if both \(H\) and \(G\) have \(\alpha\)-labelings, then each of the graphs obtained by the four graph operations on \(H\) and \(G\) has an \(\alpha\)-labeling.