Graceful labelling of the union of paths and cycles Original Research Article

Frucht and Salinas (Ars. Combin. 20 (1985) 143–157) have proved that C4 ∪ Pn is graceful, for every n⩾3, and they have conjectured that Cs ∪ Pn is graceful if n+s⩾7. In this paper we show that Cs ∪ Pn is graceful if s⩾5 and n⩾(s+5)/2.