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...

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Bibliographic Details
Main Authors: Ayesha Shabbir, Muhammad Faisal Nadeem, Tudor Zamfirescu
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/5608720
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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