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An Exploration on the Hamiltonicity of Cayley Digraphs

Bajo Calderon, Erica
http://rave.ohiolink.edu/etdc/view?acc_num=ysu161982054497591

Abstract Details

2021, Master of Science in Mathematics, Youngstown State University, Department of Mathematics and Statistics.
In 1969, Laszlo Lovasz launched a conjecture that remains open to this day. Throughout the years, variations of the conjecture have surfaced; the version we used for this study is: “Every finite connected Cayley graph is Hamiltonian”. Several studies have determined and proved Hamiltonicity for the Cayley graphs of specific types of groups with a minimal generating set. However, there are few results on the Hamiltonicity of the directed Cayley graphs. In this thesis, we look at some of the cases for which the Hamiltonicity on Cayley digraphs has been determined and we prove that the Cayley digraph of group 𝒢 such that 𝒢 = ℤp² × ℤq is non-Hamiltonian with a standard generating set.
Alexis Byers, PhD (Advisor)
Anita O'Mellan, PhD (Committee Member)
Thomas Madsen, PhD (Committee Member)
26 p.
Mathematics
Hamiltonian graph; Cayley digraph; graph theory; Hamiltonian Cayley digraph; Hamiltonian cycles

Recommended Citations

Citations

  • Bajo Calderon, E. (2021). An Exploration on the Hamiltonicity of Cayley Digraphs [Master's thesis, Youngstown State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ysu161982054497591

    APA Style (7th edition)

  • Bajo Calderon, Erica. An Exploration on the Hamiltonicity of Cayley Digraphs . 2021. Youngstown State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ysu161982054497591.

    MLA Style (8th edition)

  • Bajo Calderon, Erica. "An Exploration on the Hamiltonicity of Cayley Digraphs ." Master's thesis, Youngstown State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ysu161982054497591

    Chicago Manual of Style (17th edition)

ysu161982054497591
394
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This open access ETD is published by Youngstown State University and OhioLINK.