The Property of Hamiltonian Connectedness in Toeplitz Graphs

A spanning path in a graph G is called a Hamiltonian path. To determine which graphs possess such paths is an NP-complete problem. A graph G is called Hamiltonian-connected if any two vertices of G are connected by a Hamiltonian path. We consider here the family of Toeplitz graphs. About them, it is...

Full description

Saved in:
Bibliographic Details
Published inComplexity (New York, N.Y.) Vol. 2020; no. 2020; pp. 1 - 6
Main Authors Shabbir, Ayesha, Zamfirescu, Tudor, Nadeem, Muhammad Faisal
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
Hindawi Limited
Wiley
Subjects
Apexes
Graph theory
Graphs
Online AccessGet full text

Cover

More Information
Summary:A spanning path in a graph G is called a Hamiltonian path. To determine which graphs possess such paths is an NP-complete problem. A graph G is called Hamiltonian-connected if any two vertices of G are connected by a Hamiltonian path. We consider here the family of Toeplitz graphs. About them, it is known only for n=3 that Tnp,q is Hamiltonian-connected, while some particular cases of Tnp,q,r for p=1 and q=2,3,4 have also been investigated regarding Hamiltonian connectedness. Here, we prove that the nonbipartite Toeplitz graph Tn1,q,r is Hamiltonian-connected for all 1<q<r<n and n≥5r−2.
ISSN:1076-2787
1099-0526
DOI:10.1155/2020/5608720