Super Fibonacci graceful labeling

A Smarandache-Fibonacci Triple is a sequence S(n), n ≥ 0 such that S(n) = S(n - 1) + S(n - 2), where S(n) is the Smarandache function for integers n ≥ 0. Certainly, it is a generalization of Fibonacci sequence. A Fibonacci graceful labeling and a super Fibonacci graceful labeling on graphs were introduced by Kathiresan and Amutha in 2006. Generally, let G be a (p,q)-graph and {S(n)|n ≥ 0} a Smarandache-Fibonacci Triple. An bijection f: V(G) → {S(0), S(2), ..., S(q)} is said to be a super Smarandache-Fibonacci graceful graph if the induced edge labeling [f.sup.*] (uu) = | f(u) - f (u)| is a bijection onto the set S(2), ..., S(q)}. Particularly, if S(n), n ≥ 0 is just the Fibonacci sequence [F.sub.i], i ≥ 0, such a graph is called a super Fibonacci graceful graph. In this paper, we construct new types of graphs namely [F.sub.n] ⊕ [K.sup.+.sub.1,m], [C.sub.n] ⊕ [P.sub.m], [K.sub.1,2], [F.sub.n] ⊕ [P.sub.m] and [C.sub.n] ⊕ [K.sub.1,m] and we prove that these graphs are super Fibonacci graceful graphs. Key Words: Smarandache-Fibonacci triple, graceful labeling, Fibonacci graceful labeling, super Smarandache-Fibonacci graceful graph, super Fibonacci graceful graph. AMS(2000): 05C78