On path-sequential labellings of cycles
type: Item
instance of: scholarly article
title: On path-sequential labellings of cycles
zbMATH Open document ID: 0946.05074
DOI: 10.1016/S0012-365X(99)00226-5
author: Ron A. Fertig
published in: Discrete Mathematics
publication date: 2000-10-18T00:00:00Z
review text: Consider a labelling of the vertices of the cycle \(C_n\) by the integers \(0, 1, \ldots, n-1\), each vertex obtaining a distinct label. Such a labelling is called \(k\)-sequential, when the \(n\) sums of \(k\) adjacent labels form a set of consecutive integers. Vanderkam has conjectured that there is a \(k\)-sequential labelling of \(C_n\), if and only if \(n\) is odd, or \(k\) is odd. This paper shows that a \(k\)-sequential labelling of \(C_{mn}\) can be obtained from a \(k\)-sequential labelling of \(C_m\). This reduces the number of cases to check the conjecture considerably.
Mathematics Subject Classification ID: 05C78
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1439821
zbMATH Keywords: graph labelling
zbMATH Keywords: cycles
zbMATH Keywords: path-sequential labelling
reviewed by: Hans L. Bodlaender
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00226-5
OpenAlex ID: W2013509912
description: scientific article; zbMATH DE number 1439821