Super Fibonacci Graceful Labeling of Some Special Class of Graphs

Abstract

Abstract: 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(1), S(2),..., S(q)} is said to be a super Smarandache-Fibonacci graceful graph if the induced edge labeling f ∗ (uv) = |f(u) − f(v) | is a bijection onto the set {S(1), S(2),..., S(q)}. Particularly, if S(n), n ≥ 0 is just the Fibonacci sequence Fi, i ≥ 0, such a graph is called a super Fibonacci graceful graph. In this paper, we show that some special class of graphs namely F t n, C t n and S t m,n are super fibonacci graceful graphs