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The Property of Hamiltonian Connectedness in Toeplitz Graphs

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  • Ayesha Shabbir
  • Muhammad Faisal Nadeem
  • Tudor Zamfirescu

Abstract

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 that is Hamiltonian-connected, while some particular cases of for and have also been investigated regarding Hamiltonian connectedness. Here, we prove that the nonbipartite Toeplitz graph is Hamiltonian-connected for all and .

Suggested Citation

  • Ayesha Shabbir & Muhammad Faisal Nadeem & Tudor Zamfirescu, 2020. "The Property of Hamiltonian Connectedness in Toeplitz Graphs," Complexity, Hindawi, vol. 2020, pages 1-6, March.
    • Handle: RePEc:hin:complx:5608720
    DOI: 10.1155/2020/5608720
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