Graceful numbering of an edge-gluing of shell graphs (Q1978166)

Let \(u\) and \(v\) be two adjacent vertices in a cycle \(C_n\) of order \(n\) and let \(H(n,n-3)\) be the graph obtained by adding \(n-3\) chords incident with \(u\) in \(C_n\). The authors show that for each \(k\geq 1\) and \(n\geq 4\), the graph obtained by taking the union of \(k\) copies of \(H(n,n- 3)\) having the \(k\) edges \(uv\) identified is graceful. Reviewer's remark: Like almost all the previous papers on graceful graphs, there is absolutely no graph theory involved in this note.