Path-sequential labellings of cycles Original Research Article

We investigate labelling the vertices of the cycle of length n with the integers 0, …, n − 1 in such a way that the n sums of k adjacent integers are sequential. We show that this is impossible for both n and k even, possible for n even and k odd, and that it is possible for many cases where n is odd. We conjecture that it is always possible when n is odd.