On traceable and upper traceable numbers of graphs.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1374.05077
author: Futaba Fujie
publication date: 2016-10-26T00:00:00Z
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 6644080
zbMATH Keywords: Hamiltonian graph
zbMATH Keywords: traceable graph
zbMATH Keywords: traceable number
zbMATH Keywords: upper traceable number
MaRDI profile type: Publication
title: On traceable and upper traceable numbers of graphs.
published in: Ars Combinatoria
review text: For a connected graph \(G\) of order \(n\) at least 2 and a linear ordering \(s\) of the vertices of \(G\), \(d(s)\) is defined to be the sum of the distances between consecutive vertices of \(s\). The traceable number \(t(G)\) and the upper traceable number \(T(G)\) are defined to be the minimum and maximum, respectively, of these numbers \(d(s)\) over all linear orderings \(s\) of the vertices of \(G\). Then, for example, \(t(G)=n-1\) means that \(G\) contains a Hamiltonian path. The author investigates two realization questions for possible values of \(t(G)\) and \(T(G)\).
reviewed by: Linda Lesniak
description: scientific article; zbMATH DE number 6644080