Square graceful graphs

A ( p, q) graph G(V, E) is said to be a square graceful graph if there exists an injection f :V(G)→{0,1,2,3,..., q2 } such that the induced mapping f p : E(G) → {1, 4, 9,..., q2} defined by f (uv) | f (u) f (v) | p = − is a bijection. The function f is called a square labeling ofG. In this paper, we prove that the star n K 1, , bistarm n B , , the graph obtained by the subdivision of the edges of the star K1,n , the graph obtained by the subdivision of the central edge of the bistar Bm,n, the generalised crown n C K 3 1, Θ , graph 1 P nKmΘ(n ≥ 2) , the comb 1 P K nΘ, graph ( , ) m n P S , (3, t) kite graph (t ≥ 2) and the path Pnare square graceful graphs.