On Graceful Labeling of the Generalization of Cyclic Snakes

The aim of this paper is to present a new class of graceful graphs. In particular, we show that linear cyclic snakes (1, k) C-4-snake and (2, k) C-4-snake are graceful. We also prove that linear cyclic snakes (1, k) C-8-snake and (2, k) C-8-snake are graceful. We generalize the above results "the linear cyclic snakes (m, k) C-4-snake and (m, k) C-8-snake are graceful". Finally, we introduce a new conjecture" All the linear cyclic snakes (m, k)C-n-snakes are graceful if n = 0 (mod 4) or n = 3 (mod 4)".