Graceful numbering of an edge-gluing of shell graphs

A shell graph of order n denoted by H(n,n−3) is the graph obtained from the cycle Cn of order n by adding n−3 chords incident with a common vertex say u. Let v be a vertex adjacent to u in Cn. In this note, we shall show that for each k⩾1 and n⩾4, the graph obtained by taking the union of k copies of H(n,n−3) having the k edges uvʹs identified (see Fig. 1) is graceful.