New Classes of Graceful Graphs

Abstract

We prove the gracefulness of two classes of graphs.

Let \(G\) be a graph with \(q\) edges. \(G\) is numbered if each vertex \(v\) is assigned a non-negative integer \(\phi(v)\) and each edge \(uv\) is assigned the value \(|\phi(u) – \phi(v)|\). The numbering is called graceful if, further, the vertices are labelled with distinct integers from \(\{0, 1, 2, \ldots, q\}\) and the edges with integers from \(1\) to \(q\). A graph which admits a graceful numbering is said to be graceful. For the literature on graceful graphs see [1, 2] and the relevant references given in them.