  In this paper, we present a new sufficiency condition to obtain a graceful
labelling for every $kC_{4n}$ snake and use this condition to label every such
snake for $n=1,2,\ldots,6$. Then, we extend this result to cyclic snakes where
the cycles lengths vary. Also, we obtain new results on the (near) graceful
labelling of cyclic snakes based on cycles of lengths $n=6, 10, 14$, completely
solving the case $n=6$.

Combinatorics