On path-sequential labellings of cycles Original Research Article

A k-sequential labelling of the cycle Cn is a labelling of its vertices with the integers {0,1,…,n−1} such that the n sums of k adjacent labels themselves form a set of consecutive integers. By demonstrating that a k-sequential labelling of Cmn can be obtained from a k-sequential labelling of Cn, we make significant progress toward proof of a conjecture of Vanderkam which states that such a labelling is possible if and only if n and k are not both even.