Graceful Labelings of Cyclic Snakes

In this paper we present graceful and nearly graceful labelings of some graphs. In particular, we show, graceful labelings of the \(kC_4-snake\) (for the general case),\(kC_6\) and \(kC_{12}-snakes\) (for the even case),and also establish some conditions to obtain graceful labelings of \(kC_{4n}-snakes\) with some related results. Moreover, for the linear \(kC_6\)-snake, we show:a graceful labeling when \(k\) is even,a nearly graceful labeling when \(k\) is odd.We also explore the connection of these labelings with more restrictive variations of graceful ones.