Prime Graceful Labeling - Hameed Hassan, T.; Mohammad Abbas, R. (International Journal of Engineering and Technology, 2018)
A graph G with m vertices and n edges, is said to be prime graceful labeling, if there is an injectionÂ Â from the vertices of G to 1, 2, ..., k where k = min 2m, 2n such thatÂ gcd ( ( ),Â ( )=1 and the induced injective functionÂ Â from the edges of G to 1, 2, ..., k âˆ’ 1 defined by Â ( ) = | Â ( ) âˆ’ ( ) | , the resulting edge labels are distinct. In this paper path Â , cycle Cn , star K1,n , friendship graph Fn , bistar Bn,n, C4 âˆª Pn , Km,2 and Km,2 âˆª Pn are shown to be Prime Graceful Labeling .Â